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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.52 no.1 Bogotá Jan./June 2018

https://doi.org/10.15446/recolma.v51n2.74529 

Original articles

Orthogonal Decomposition in Omega-Weighted Classes of Functions Subharmonic in the Half-Plane

Descomposición ortogonal de funciones subharmónicas en el semiplano por medio de clases omega-pesadas

Armen Jerbashian1  * 

Daniel Vargas2 

1 Universidad de Antioquia, Medellín - Colombia

2 Universidad de Antioquia, Medellín - Colombia


Abstract:

The paper gives a harmonic, (-weighted, half-plane analog of W. Wirtinger's projection theorem and its (1-r)(-weighted extension by M. Djrbashian and also an orthogonal decomposition for some classes of functions subharmonic in the half-plane.

Keywords: Subharmonic functions; orthogonal decomposition; potentials

Resumen:

El artículo da un análogo armónico (-pesado en el semiplano del teorema de proyección de W. Wirtinger y su extensión (1-r)(-pesada establecida por M. Djrbashian. También es hallada una descomposición ortogonal para algunas clases de funciones subarmónicas en el semiplano.

Palabras clave: Funciones subarmónicas; descomposición ortogonal; potenciales

Text complete end PDF

References

1. Djrbashian, M., On the representability problem of analytic functions, Soobsch. Inst. Matem. i Mekh. Akad. Nauk Arm. SSR 2 (1948). [ Links ]

2. Jerbashian, A., Functions of a-Bounded Type in the Half-Plane, Advances in Complex Analysis and Applications, Springer, 2005. [ Links ]

3. Jerbashian, A., On Ap (,( Spaces in the Half-Plane, in: Operator Theory: Advances and Applications 158 (2005), 141-158, Birkhäuser Verlag, Basel/Switzerland. [ Links ]

4. Jerbashian, A., Orthogonal decomposition of functions subharmonic in the unit disc, in: Operator Theory: Advances and Applications 190 (2009), 335-340, Birkhäuser Verlag, Basel/Switzerland. [ Links ]

5. Jerbashian, A. and Jerbashian, V., Functions of (-bounded type in the half-plane, Calculation Methods and Function Theory (CMFT) 7 (2007), no. 2, 205-238. [ Links ]

6. Koosis, P., Introduction to Hp spaces, Cambridge University Press, 1998. [ Links ]

7. Walsh, J., Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc. Coll. Publ. XX, Edwards Brothers, Inc., Ann Arbor, Michigan, 1956. [ Links ]

8. Wirtinger, W., Über eine Minimumaufgabe im Gebiet der analytischen Functionen, Monatshefte für Math. und Phys. 39 (1932). [ Links ]

Received: April 01, 2017; Accepted: December 06, 2017

*Correspondencia: Armen Jerbashian, Instituto de Matemáticas, Universidad de Medellín, Facultad de Ciencias Exactas y Naturales, Calle 67 No. 53 - 108, Medellín - Colombia. Correo electrónico: armenjerbashian@yahoo.com. DOI: https://doi.org/10.15446/recolma.v51n2.74529

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License