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Representing systems for the space of holomorphic functions in a (ρ,α)-convex domain

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Abstract

This article is a natural supplement to Chapter 5 ofAsymptotic Characteristics of Entire Functions and Their Applications [Nauka, Novosibirsk (1991)]. Earlier, for the functions holomorphic in the closure of a (ρ,α)-convex bounded domain D, the author found a criterion of the existence of a series expansion in a special system of entire functions. Here it is shown that the same criterion applies to the functions holomorphic in D. Moreover, a new integral representation of entire functions is described, which enables one to construct new representing systems for the spaces of holomorphic functions\(H(\overline D )\) and H(D). Bibliography: 17 titles.

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Authors
  1. L. S. Maergoîz
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 206, 1993, pp. 91–196.

Translated by D. V. Yakubowich.

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Maergoîz, L.S. Representing systems for the space of holomorphic functions in a (ρ,α)-convex domain. J Math Sci 80, 1931–1940 (1996). https://doi.org/10.1007/BF02367008

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