Approximation of the Muntz-Szasz Type in Weight Spaces L-p and Zeroes of Functions of Bergman Classes in a Half-Plane

被引：0

作者：

Sedletskii, A. M. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Main Bldg,GSP 1 Vorobyovy Gory, Moscow 119991, Russia

来源：

RUSSIAN MATHEMATICS | 2008年 / 52卷 / 05期

基金：

俄罗斯基础研究基金会;

关键词：

the Szasz theorem; the completeness of the system of exponents on a semiaxis; Bergman classes; zeroes of analytic functions;

D O I：

10.3103/S1066369X08050101

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the completeness of the system of exponents exp(-lambda(n)t), Re lambda(n) > 0, in spaces L-p with the power weight on the semiaxis R+. We prove a sufficient condition for the completeness; one can treat it as a modification of the well-known Szasz condition. With p = 2 it is unimprovable (in a sense). The proof is based on the results (which are also obtained in this paper) on the distribution of zeroes of functions of the Bergman classes in a half-plane.

引用

页码：80 / 87

页数：8

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