<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2019000200219</article-id>
<article-id pub-id-type="doi">10.18273/revint.v37n2-2019002</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[On the nuclear trace of Fourier integral operators]]></article-title>
<article-title xml:lang="es"><![CDATA[Sobre la traza nuclear de operadores integrales de Fourier]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cardona]]></surname>
<given-names><![CDATA[Duván]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Ghent University  ]]></institution>
<addr-line><![CDATA[Ghent ]]></addr-line>
<country>Belgium</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<volume>37</volume>
<numero>2</numero>
<fpage>219</fpage>
<lpage>249</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2019000200219&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2019000200219&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2019000200219&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this paper we characterise the r-nuclearity of Fourier integral operators on Lebesgue spaces. Fourier integral operators will be considered in &#8477;n, the discrete group &#8484;n, the n-dimensional torus and symmetric spaces (compact homogeneous manifolds). We also give formulae for the nuclear trace of these operators. Explicit examples will be given on &#8484;n, the torus &#120139;n, the special unitary group SU(2), and the projective complex plane &#8450;&#8473;2. Our main theorems will be applied to the characterization of r-nuclear pseudo-differential operators defined by the Weyl quantization procedure. MSC2010: 58J40; 47B10, 47G30, 35S30.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En esta investigación se caracteriza la r-nuclearidad de operadores integrales de Fourier en espacios de Lebesgue. Las nociones de traza nuclear y operador nuclear sobre espacios de Banach son conceptos análogos a aquellas de traza espectral y de operador de clase traza en espacios de Hilbert. Operadores integrales de Fourier, por otro lado, surgen para expresar soluciones a problemas de Cauchy hiperbólicos o para estudiar la función espectral asociada a un operador geométrico sobre una variedad diferenciable. Los operadores integrales de Fourier se consideran actuando sobre &#8477;n, el grupo discreto &#8484;n, el toro de dimensión n y finalmente, espacios simétricos (variedades compactas homogéneas). Se presentan ejemplos explícitos de tales caracterizaciones sobre &#8484;n, el grupo especial unitario SU(2), y el plano complejo proyectivo &#8450;&#8473;2. Los resultados principales de la presente investigación se aplican en la caracterización de operadores pseudo diferenciales nucleares definidos mediante el proceso de cuantificación de Weyl.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Fourier integral operator]]></kwd>
<kwd lng="en"><![CDATA[nuclear operator]]></kwd>
<kwd lng="en"><![CDATA[nuclear trace]]></kwd>
<kwd lng="en"><![CDATA[spectral trace]]></kwd>
<kwd lng="en"><![CDATA[compact homogeneous manifold]]></kwd>
<kwd lng="es"><![CDATA[Operador integral de Fourier]]></kwd>
<kwd lng="es"><![CDATA[operador nuclear]]></kwd>
<kwd lng="es"><![CDATA[traza nuclear]]></kwd>
<kwd lng="es"><![CDATA[traza espectral]]></kwd>
<kwd lng="es"><![CDATA[variedad compacta homogénea]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>[1]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Akylzhanov]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Nursultanov]]></surname>
<given-names><![CDATA[E]]></given-names>
</name>
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Hardy-Littlewood, Hausdorff-Young-Paley inequalities, and Lp - Lq Fourier multipliers on compact homogeneous manifolds]]></article-title>
<source><![CDATA[arXiv]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B2">
<label>[2]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Asada]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Fujiwara]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On some oscillatory integral transformations in L2(Rn)]]></article-title>
<source><![CDATA[Japan J. Math]]></source>
<year>1978</year>
<volume>4</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>299-361</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>[3]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Barraza]]></surname>
<given-names><![CDATA[E.S.]]></given-names>
</name>
<name>
<surname><![CDATA[Cardona]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On nuclear Lp-multipliers associated to the Harmonic oscillator]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<source><![CDATA[Analysis in Developing Countries, Springer Proceedings in Mathematics &amp; Statistics]]></source>
<year>2018</year>
<page-range>31-41</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<label>[4]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bronzan]]></surname>
<given-names><![CDATA[J. B]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Parametrization of SU(3)]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>1988</year>
<volume>38</volume>
<numero>6</numero>
<issue>6</issue>
</nlm-citation>
</ref>
<ref id="B5">
<label>[5]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Botchway]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Kibiti]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Difference equations and pseudo-differential operators on Zn]]></article-title>
<source><![CDATA[arXiv]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B6">
<label>[6]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Buzano]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Toft]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Schatten-von Neumann properties in the Weyl calculus]]></article-title>
<source><![CDATA[J. Funct.Anal]]></source>
<year>2010</year>
<volume>259</volume>
<numero>12</numero>
<issue>12</issue>
<page-range>3080-114</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>[7]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cardona]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Barraza]]></surname>
<given-names><![CDATA[E.S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Characterization of nuclear pseudo-multipliers associated to the harmonic oscillator]]></article-title>
<source><![CDATA[UPB, Scientific Bulletin, Series A: Applied Mathematics and Physics]]></source>
<year>2018</year>
<volume>80</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>163-72</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>[8]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cardona]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A brief description of operators associated to the quantum harmonic oscillator on Schatten-von Neumann classes]]></article-title>
<source><![CDATA[Rev. Integr. temas mat]]></source>
<year>2018</year>
<volume>36</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>49-57</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>[9]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cardona]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Nuclear pseudo-differential operators in Besov spaces on compact Lie groups]]></article-title>
<source><![CDATA[J. Fourier Anal. Appl]]></source>
<year>2017</year>
<volume>23</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>1238-62</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>[10]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Coriasco]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the boundedness of Fourier integral operators on Lp(&#8477;n)]]></article-title>
<source><![CDATA[C. R. Math. Acad. Sci. Paris]]></source>
<year>2010</year>
<volume>348</volume>
<numero>15-16</numero>
<issue>15-16</issue>
<page-range>847-51</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>[11]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Coriasco]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Global Lp continuity of Fourier integral operators]]></article-title>
<source><![CDATA[Trans. Amer. Math. Soc]]></source>
<year>2014</year>
<volume>366</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>2575-96</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>[12]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Estimations Lp pour une classe d'opfateurs pseudo-differentiels dans le cadre du calcul de Weyl-Hormander]]></article-title>
<source><![CDATA[J. Anal. Math]]></source>
<year>2006</year>
<volume>100</volume>
<page-range>337-74</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>[13]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A trace formula for nuclear operators on Lp]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Schulze]]></surname>
<given-names><![CDATA[B.W.]]></given-names>
</name>
<name>
<surname><![CDATA[Wong]]></surname>
<given-names><![CDATA[M.W]]></given-names>
</name>
</person-group>
<source><![CDATA[textit Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations, Operator Theory: Advances and Applications]]></source>
<year>2009</year>
<volume>205</volume>
<page-range>181-93</page-range><publisher-name><![CDATA[Birkhäuser Basel]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<label>[14]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Wong]]></surname>
<given-names><![CDATA[M.W]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Lp-nuclear pseudo-differential operators on Z and S1]]></article-title>
<source><![CDATA[Proc. Amer. Math. Soc]]></source>
<year>2013</year>
<volume>141</volume>
<numero>11</numero>
<issue>11</issue>
<page-range>3935-394</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>[15]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The trace of nuclear operators on Lp(&#956;) for &#963;-finite Borel measures on second countable spaces]]></article-title>
<source><![CDATA[Integral Equations Operator Theory]]></source>
<year>2010</year>
<volume>68</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>61-74</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>[16]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Lp-nuclearity, traces, and Grothendieck-Lidskii formula on compact Lie groups]]></article-title>
<source><![CDATA[J. Math. Pures Appl]]></source>
<year>2014</year>
<volume>9</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>153-72</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>[17]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Schatten classes on compact manifolds: Kernel conditions]]></article-title>
<source><![CDATA[J. Funct. Anal]]></source>
<year>2014</year>
<volume>267</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>772-98</page-range></nlm-citation>
</ref>
<ref id="B18">
<label>[18]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds]]></article-title>
<source><![CDATA[C. R. Acad. Sci. Paris. Ser. I]]></source>
<year>2014</year>
<volume>352</volume>
<numero>10</numero>
<issue>10</issue>
<page-range>779-84</page-range></nlm-citation>
</ref>
<ref id="B19">
<label>[19]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Fourier multipliers, symbols and nuclearity on compact manifolds]]></article-title>
<source><![CDATA[J. Anal. Math]]></source>
<year>2018</year>
<volume>135</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>757-800</page-range></nlm-citation>
</ref>
<ref id="B20">
<label>[20]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The bounded approximation property of variable Lebesgue spaces and nuclearity]]></article-title>
<source><![CDATA[Math. Scand]]></source>
<year>2018</year>
<volume>122</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>299-319</page-range></nlm-citation>
</ref>
<ref id="B21">
<label>[21]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Schatten classes and traces on compact groups]]></article-title>
<source><![CDATA[Math. Res. Lett]]></source>
<year>2017</year>
<volume>24</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>979-1003</page-range></nlm-citation>
</ref>
<ref id="B22">
<label>[22]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[B]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Approximation property and nuclearity on mixed-norm Lp, modulation and Wiener amalgam spaces]]></article-title>
<source><![CDATA[J. Lond. Math. Soc]]></source>
<year>2016</year>
<volume>94</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>391-408</page-range></nlm-citation>
</ref>
<ref id="B23">
<label>[23]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[B]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Grothendieck-Lidskii trace formula for mixed-norm and variable Lebesgue spaces]]></article-title>
<source><![CDATA[J. Spectr. Theory]]></source>
<year>2016</year>
<volume>6</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>781-91</page-range></nlm-citation>
</ref>
<ref id="B24">
<label>[24]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Tokmagambetov]]></surname>
<given-names><![CDATA[N]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Schatten classes, nuclearity and non-harmonic analysis on compact manifolds with boundary]]></article-title>
<source><![CDATA[J. Math. Pures Appl]]></source>
<year>2017</year>
<volume>9</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>758-83</page-range></nlm-citation>
</ref>
<ref id="B25">
<label>[25]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Duistermaat]]></surname>
<given-names><![CDATA[J.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Hörmander]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Fourier integral operators. II]]></article-title>
<source><![CDATA[Acta Math]]></source>
<year>1972</year>
<volume>128</volume>
<numero>3-4</numero>
<issue>3-4</issue>
<page-range>183-269</page-range></nlm-citation>
</ref>
<ref id="B26">
<label>[26]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Eskin]]></surname>
<given-names><![CDATA[G. I]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Degenerate elliptic pseudodifferential equations of principal type]]></article-title>
<source><![CDATA[Mat. Sb. (N.S.)]]></source>
<year>1970</year>
<volume>82</volume>
<numero>124</numero>
<issue>124</issue>
<page-range>585-628</page-range></nlm-citation>
</ref>
<ref id="B27">
<label>[27]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fegan]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
</person-group>
<source><![CDATA[Introduction to compact Lie groups. Series in Pure Mathematics]]></source>
<year>1991</year>
<volume>13</volume>
<publisher-loc><![CDATA[NJ ]]></publisher-loc>
<publisher-name><![CDATA[World Scientific Publishing Co., Inc., River Edge]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B28">
<label>[28]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fujiwara]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[construction of the fundamental solution for the Schrödinger equations]]></article-title>
<source><![CDATA[Proc.Japan Acad. Ser. A Math. Sci]]></source>
<year>1979</year>
<volume>55</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>10-4</page-range></nlm-citation>
</ref>
<ref id="B29">
<label>[29]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ghaemi]]></surname>
<given-names><![CDATA[M.B.]]></given-names>
</name>
<name>
<surname><![CDATA[Jamalpour Birgani]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Wong]]></surname>
<given-names><![CDATA[M.W]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Characterizations of nuclear pseudo-differential operators on S1 with applications to adjoints and products]]></article-title>
<source><![CDATA[J. Pseudo-Differ. Oper. Appl]]></source>
<year>2017</year>
<volume>8</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>191-201</page-range></nlm-citation>
</ref>
<ref id="B30">
<label>[30]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ghaemi]]></surname>
<given-names><![CDATA[M.B]]></given-names>
</name>
<name>
<surname><![CDATA[Jamalpour Birgani]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Wong]]></surname>
<given-names><![CDATA[M.W]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Characterization, adjoints and products of nuclear pseudo-differential operators on compact and Hausdorff groups]]></article-title>
<source><![CDATA[U.P.B. Sci. Bull., Series A]]></source>
<year>2017</year>
<volume>79</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>207-20</page-range></nlm-citation>
</ref>
<ref id="B31">
<label>[31]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Grothendieck]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<source><![CDATA[Produits tensoriels topologiques et espaces nucléaires]]></source>
<year>1955</year>
<volume>16</volume>
<publisher-name><![CDATA[Memoirs Amer. Math. Soc]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B32">
<label>[32]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hörmander]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Fourier integral operators I]]></article-title>
<source><![CDATA[Acta Math]]></source>
<year>1971</year>
<volume>127</volume>
<numero>1-2</numero>
<issue>1-2</issue>
<page-range>79-183</page-range></nlm-citation>
</ref>
<ref id="B33">
<label>[33]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hörmander]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Pseudo-differential Operators and Hypo-elliptic equations]]></article-title>
<source><![CDATA[Amer. Math. Soc]]></source>
<year>1967</year>
<volume>10</volume>
<page-range>138-83</page-range></nlm-citation>
</ref>
<ref id="B34">
<label>[34]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hörmander]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
</person-group>
<source><![CDATA[The Analysis of the linear partial differential operators, III]]></source>
<year>1985</year>
<publisher-loc><![CDATA[Berlin ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B35">
<label>[35]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kumano-go]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A calculus of Fourier integral operators on &#8477;n and the fundamental solution for an operator of hyperbolic type]]></article-title>
<source><![CDATA[Comm. Partial Differential Equations]]></source>
<year>1976</year>
<volume>1</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-44</page-range></nlm-citation>
</ref>
<ref id="B36">
<label>[36]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jamalpour Birgani]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Characterizations of Nuclear Pseudo-differential Operators on Z with some Applications]]></article-title>
<source><![CDATA[Math. Model. of Nat. Phenom]]></source>
<year>2018</year>
<volume>13</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>13-30</page-range></nlm-citation>
</ref>
<ref id="B37">
<label>[37]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Miyachi]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On some estimates for the wave equation in Lp and Hp]]></article-title>
<source><![CDATA[J. Fac. Sci. Univ. Tokyo Sect. IA Math]]></source>
<year>1980</year>
<volume>27</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>331-54</page-range></nlm-citation>
</ref>
<ref id="B38">
<label>[38]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Molahajloo]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Pseudo-differential Operators on &#8484;]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Schulze]]></surname>
<given-names><![CDATA[B.W.]]></given-names>
</name>
<name>
<surname><![CDATA[Wong]]></surname>
<given-names><![CDATA[M.W]]></given-names>
</name>
</person-group>
<source><![CDATA[textitPseudo-Differential Operators: Complex Analysis and Partial Differential Equations, Operator Theory: Advances and Applications]]></source>
<year>2009</year>
<volume>205</volume>
<page-range>213-21</page-range><publisher-name><![CDATA[Birkhäuser Basel]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B39">
<label>[39]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Peral]]></surname>
<given-names><![CDATA[J.C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Lp-estimates for the wave equation]]></article-title>
<source><![CDATA[J. Funct. Anal]]></source>
<year>1980</year>
<volume>36</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>114-45</page-range></nlm-citation>
</ref>
<ref id="B40">
<label>[40]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pietsch]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<source><![CDATA[Operator ideals]]></source>
<year>1978</year>
<publisher-loc><![CDATA[VEB Deutscher Verlag der Wissenschaften, Berlin ]]></publisher-loc>
<publisher-name><![CDATA[Mathematische Monographien]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B41">
<label>[41]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pietsch]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<source><![CDATA[History of Banach spaces and linear operator]]></source>
<year>2007</year>
<publisher-loc><![CDATA[Boston, MA ]]></publisher-loc>
<publisher-name><![CDATA[Birkhäuser Boston, Inc]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B42">
<label>[42]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Reinov]]></surname>
<given-names><![CDATA[O.I.]]></given-names>
</name>
<name>
<surname><![CDATA[Latif]]></surname>
<given-names><![CDATA[Q]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Grothendieck-Lidskii theorem for subspaces of Lp-spaces]]></article-title>
<source><![CDATA[Math. Nachr]]></source>
<year>2013</year>
<volume>286</volume>
<numero>2-3</numero>
<issue>2-3</issue>
<page-range>279-82</page-range></nlm-citation>
</ref>
<ref id="B43">
<label>[43]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nicola]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Rodino]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Dixmier traceability for general pseudo-differential operators C]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Burghelea]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Melrose]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Mishchenko]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Troitsky]]></surname>
<given-names><![CDATA[E]]></given-names>
</name>
</person-group>
<source><![CDATA[*-algebras and elliptic theory II, Trends Math]]></source>
<year>2008</year>
<page-range>227-37</page-range><publisher-name><![CDATA[Birkhäuser Basel]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B44">
<label>[44]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Sugimoto]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Global L2-boundedness theorems for a class of Fourier integral operators]]></article-title>
<source><![CDATA[Comm. Partial Differential Equations]]></source>
<year>2006</year>
<volume>31</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>547-69</page-range></nlm-citation>
</ref>
<ref id="B45">
<label>[45]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Sugimoto]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A smoothing property of Schrödinger equations in the critical case]]></article-title>
<source><![CDATA[Math. Ann]]></source>
<year>2006</year>
<volume>335</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>645-73</page-range></nlm-citation>
</ref>
<ref id="B46">
<label>[46]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Sugimoto]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Weighted Sobolev L2 estimates for a class of Fourier integral operators]]></article-title>
<source><![CDATA[Math. Nachr]]></source>
<year>2011</year>
<volume>284</volume>
<numero>13</numero>
<issue>13</issue>
<page-range>1715-38</page-range></nlm-citation>
</ref>
<ref id="B47">
<label>[47]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Sugimoto]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Global regularity properties for a class of Fourier integral operators]]></article-title>
<source><![CDATA[arxiv]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B48">
<label>[48]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Turunen]]></surname>
<given-names><![CDATA[V]]></given-names>
</name>
</person-group>
<source><![CDATA[Pseudo-differential Operators and Symmetries: Background Analysis and Advanced Topics]]></source>
<year>2010</year>
<publisher-loc><![CDATA[Basel ]]></publisher-loc>
<publisher-name><![CDATA[Birkhaüser-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B49">
<label>[49]</label><nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Wirth]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<source><![CDATA[Dispersive type estimates for Fourier integrals and applications to hyperbolic systems]]></source>
<year>2011</year>
<conf-name><![CDATA[ Conference Publications]]></conf-name>
<conf-loc> </conf-loc>
<page-range>1263-70</page-range></nlm-citation>
</ref>
<ref id="B50">
<label>[50]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruzhansky]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<source><![CDATA[Regularity theory of Fourier integral operators with complex phases and singularities of affine fibrations]]></source>
<year>2001</year>
<volume>131 of CWI Tract</volume>
<publisher-loc><![CDATA[Amsterdam ]]></publisher-loc>
<publisher-name><![CDATA[Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B51">
<label>[51]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Seeger]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Sogge]]></surname>
<given-names><![CDATA[C.D.]]></given-names>
</name>
<name>
<surname><![CDATA[Stein]]></surname>
<given-names><![CDATA[E.M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Regularity properties of Fourier integral operators]]></article-title>
<source><![CDATA[Ann. of Math]]></source>
<year>1991</year>
<volume>134</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>231-51</page-range></nlm-citation>
</ref>
<ref id="B52">
<label>[52]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tao]]></surname>
<given-names><![CDATA[T]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The weak-type (1,1) of Fourier integral operators of order - (n - 1)/2]]></article-title>
<source><![CDATA[J. Aust. Math. Soc]]></source>
<year>2004</year>
<volume>76</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-21</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
