The Schauder basis in the solution space of a homogeneous convolution equation
type: Item
instance of: scholarly article
title: The Schauder basis in the solution space of a homogeneous convolution equation
zbMATH Open document ID: 0906.46007
DOI: 10.1007/BF02309393
author: A. S. Krivosheev
published in: Mathematical Notes
publication date: 1996-02-21T00:00:00Z
review text: As stated in the title, the author shows that the solution space of a homogeneous convolution equation has a Schauder basis. More precisely, let \(D\) be a convex domain in the complex plane \(C\), and let \(u\) be an analytic functional of \(H^*(D)\) where \(H(D)\) is the space of analytic functions in \(D\) with uniform topology on compact sets of \(D\). Suppose the Laplace transform \( f(z)=(u,\text{exp } \lambda z)\) satisfies certain regularity conditions. Then the solution space \(W(D,u)\) of the convolution equation \((u,f(z+y))=0\) has a Schauder basis. This generalizes an earlier result in \textit{V. V. Napalkov} [Mat. Zametki 43, No. 1, 44-55 (1988; Zbl 0651.46014)] where stronger conditions were required.
Mathematics Subject Classification ID: 46B15
Mathematics Subject Classification ID: 46F15
Mathematics Subject Classification ID: 46E10
zbMATH DE Number: 846459
zbMATH Keywords: Schauder basis
zbMATH Keywords: convolution equations
zbMATH Keywords: solution space
zbMATH Keywords: homogeneous convolution
zbMATH Keywords: convex domain
zbMATH Keywords: analytic functional
zbMATH Keywords: space of analytic functions
zbMATH Keywords: uniform topology on compact sets
zbMATH Keywords: Laplace transform
reviewed by: Peng-Yee Lee
MaRDI profile type: Publication
cites work: Q3704481
cites work: Q3848344
cites work: Q5613420
cites work: Q3796192
cites work: Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals.
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description: scientific article; zbMATH DE number 846459