Bepresentating systems of the space of functions holomorphic in a~$(\rho,\alpha)$-convex domain
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 21, Tome 206 (1993), pp. 91-106
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This article is a natural supplement to Chapter 5 of [8]. We show that the criterion (found earlier) of decomposability of functions holomorphic in the closure of a $(\rho,\alpha)$-convex domain $D$ into a series against a sertain special system of entire functions applies also to the functions holomorphic in $D$. Moreover, a new integral representation of entire functions is presented that enables one to construct new representating systems for the spaces of holomorphic functions $H(\overline D)$ and $H(D)$. Bibliography: 17 titles.
@article{ZNSL_1993_206_a7,
author = {L. S. Maergoiz},
title = {Bepresentating systems of the space of functions holomorphic in a~$(\rho,\alpha)$-convex domain},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {91--106},
publisher = {mathdoc},
volume = {206},
year = {1993},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1993_206_a7/}
}
TY - JOUR AU - L. S. Maergoiz TI - Bepresentating systems of the space of functions holomorphic in a~$(\rho,\alpha)$-convex domain JO - Zapiski Nauchnykh Seminarov POMI PY - 1993 SP - 91 EP - 106 VL - 206 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1993_206_a7/ LA - ru ID - ZNSL_1993_206_a7 ER -
L. S. Maergoiz. Bepresentating systems of the space of functions holomorphic in a~$(\rho,\alpha)$-convex domain. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 21, Tome 206 (1993), pp. 91-106. http://geodesic.mathdoc.fr/item/ZNSL_1993_206_a7/