Abstract

CARDONA, Duván. On the nuclear trace of Fourier integral operators. Integración - UIS [online]. 2019, vol.37, n.2, pp.219-249.  Epub Oct 10, 2019. ISSN 0120-419X.  https://doi.org/10.18273/revint.v37n2-2019002.

In this paper we characterise the r-nuclearity of Fourier integral operators on Lebesgue spaces. Fourier integral operators will be considered in ℝn, the discrete group ℤn, 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 ℤn, the torus 𝕋n, the special unitary group SU(2), and the projective complex plane ℂℙ2. 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.

Keywords : Fourier integral operator; nuclear operator; nuclear trace; spectral trace; compact homogeneous manifold.

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