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May 2008 Weighted integral representations of entire functions of several complex variables
Arman H. Karapetyan
Bull. Belg. Math. Soc. Simon Stevin 15(2): 287-302 (May 2008). DOI: 10.36045/bbms/1210254826

Abstract

In the paper we consider the spaces of entire functions $f(z), z\in C^n$, satisfying the condition $$ \int_{R^n}\left(\int_{R^n}|f(x+iy)|^p dx \right)^s |y|^{\alpha}e^{-\sigma |y|^{\rho}}dy <+\infty . $$ For these classes the following integral representation is obtained: $$ f(z)=\int_{C^n}f(u+iv)\Phi(z,u+iv)|v|^{\alpha}e^{-\sigma |v|^{\rho}}dudv ,\quad z\in C^n ,$$ where the reproducing kernel $\Phi(z,u+iv)$ is written in an explicit form as a Fourier type integral. Also, an estimate for $\Phi$ is obtained.

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Arman H. Karapetyan. "Weighted integral representations of entire functions of several complex variables." Bull. Belg. Math. Soc. Simon Stevin 15 (2) 287 - 302, May 2008. https://doi.org/10.36045/bbms/1210254826

Information

Published: May 2008
First available in Project Euclid: 8 May 2008

zbMATH: 1147.32007
MathSciNet: MR2424114
Digital Object Identifier: 10.36045/bbms/1210254826

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Rights: Copyright © 2008 The Belgian Mathematical Society

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Vol.15 • No. 2 • May 2008
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