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.
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页码：613 / 623
页数：11
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