Factoring an entire function into two `almost equal' functions
type: Item
instance of: scholarly article
title: Factoring an entire function into two `almost equal' functions
zbMATH Open document ID: 0868.30030
DOI: 10.1007/BF02674639
author: R. S. Yulmukhametov
published in: Siberian Mathematical Journal
publication date: 1997-07-22T00:00:00Z
review text: The article is concerned with factoring an entire function on the complex plane into the product of two entire functions with almost the same growth at infinity. The main result establishes such a factorization under rather general but bulky conditions. It is concretized in the case when the zeros of the function in question lie in some horizontal strip. As an application, a smooth compactly-supported function on the real axis, having the Fourier-Laplace transform with zeros in a horizontal strip, is proved to be representable as the convolution of two other smooth compactly-supported functions. This gives a partial answer to Ehrenpreis's factorization problem in the algebra of smooth compactly-supported functions of one variable.
Mathematics Subject Classification ID: 30D20
Mathematics Subject Classification ID: 42-XX
zbMATH DE Number: 1037950
zbMATH Keywords: convolution
zbMATH Keywords: Fourier transform
zbMATH Keywords: division problem
MaRDI profile type: Publication
cites work: Solution of Some Problems of Division. Part IV. Invertible and Elliptic Operators
cites work: Q4173774
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cites work: Q3784370
cites work: Approximation of subharmonic functions
full work available at URL: https://doi.org/10.1007/bf02674639
OpenAlex ID: W2038854940
description: scientific article; zbMATH DE number 1037950