Fourier transform of invariant differential operators on a locally- compact abelian group
type: Item
instance of: scholarly article
title: Fourier transform of invariant differential operators on a locally- compact abelian group
zbMATH Open document ID: 0836.43006
DOI: 10.1007/BF02110745
published in: Mathematical Notes
publication date: 1996-01-08T00:00:00Z
review text: Let \(X\) be an LCA group and \(G\) its dual group. A function \(p : G \to \mathbb{C}\) is called a polynomial if its restriction \(p|_H\) to each compactly generated closed subgroup \(H \subset G\) can be represented as an ordinary polynomial of a finite collection of real characters of \(H\). The author proves for \(X\) a group analog of the following well known result: The Fourier transform turns any differential operator with constant coefficients on \(\mathbb{R}^n\) into an operator of multiplication by a polynomial.
Mathematics Subject Classification ID: 43A25
Mathematics Subject Classification ID: 43A70
zbMATH DE Number: 830713
zbMATH Keywords: LCA group
zbMATH Keywords: polynomial
zbMATH Keywords: real characters
zbMATH Keywords: Fourier transform
zbMATH Keywords: differential operator
zbMATH Keywords: operator
author: Sergei S. Akbarov
MaRDI profile type: Publication
cites work: Q3803619
cites work: Q4405003
cites work: Realizability Theory of Continuous Linear Operators on Groups
description: scientific article; zbMATH DE number 830713