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.
Publié le : 2008-05-15
Classification:
weighted spaces of entire functions,
Paley-Wiener type theorems,
reproducing kernels,
weighted integral representations,
32A15,
32A25,
32A37,
26D15,
30D10,
30E20,
42B10,
44A10
@article{1210254826,
author = {Karapetyan, Arman H.},
title = {Weighted integral representations of entire functions of several complex variables},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {15},
number = {1},
year = {2008},
pages = { 287-302},
language = {en},
url = {http://dml.mathdoc.fr/item/1210254826}
}
Karapetyan, Arman H. Weighted integral representations of entire functions of several complex variables. Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, pp. 287-302. http://gdmltest.u-ga.fr/item/1210254826/