Perturbations of an Integer Sequence as Zero Sets of Divisors in Some Spaces of Entire Functions

被引：1

作者：

Abuzyarova, N. F. ^{[1
,2
]}

机构：

[1] Ufa Univ Sci & Technol, Ufa 450076, Russia

[2] Russian Acad Sci, Inst Math Comp Ctr, Subdiv Ufa Fed Res Ctr, Ufa 450008, Russia

来源：

MATHEMATICAL NOTES | 2023年 / 113卷 / 5-6期

基金：

俄罗斯科学基金会;

关键词：

ultradistribution; zero set; entire function; division theorem; Fourier-Laplace transform; convolution operator; EHRENPREIS; SENSE;

D O I：

10.1134/S0001434623050012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider weighted spaces of entire functions obtained as the images of spaces of ultradistributions of minimal type and normal type on the real line under the Fourier-Laplace transform. The divisors of these spaces are studied. Namely, we find conditions on a perturbing sequence under which the sequence of integers perturbed by it will be the zero set of an entire function that is a divisor of one of the above-mentioned spaces.

引用

页码：613 / 623

页数：11

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