Weighted integral representations of entire functions of several complex variables
Karapetyan, Arman H.
Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, p. 287-302 / Harvested from Project Euclid
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/