On a linear functional equation
type: Item
instance of: scholarly article
title: On a linear functional equation
zbMATH Open document ID: 0686.39012
DOI: 10.1007/BF01839998
published in: Aequationes Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137320
review text: The equation reads: \(f(x+ny)+\sum^{n-1}_{k=0}c_ k(y)f(x+ky)=0,\) where n is a fixed positive integer and \(c_ 0,...,c_{n-1}\) are given complex-valued functions defined on a group G. If G is either a finitely generated discrete Abelian group, or G is a locally compact compactly generated Abelian group in which the set of all compact elements is connected, then each continuous solution \(f:G\to {\mathbb{C}}\) is an exponential polynomial. This means that f is a linear combination of exponential functions (i.e. continuous homomorphisms of G into the multiplicative group of nonzero complex numbers) with (continuous) polynomial coefficients.
reviewed by: Karol Baron
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 43A25
zbMATH DE Number: 4124296
zbMATH Keywords: locally compact Abelian group
zbMATH Keywords: exponential function
zbMATH Keywords: polynomial function
zbMATH Keywords: Fourier transform
author: László Székelyhidi
MaRDI profile type: Publication
cites work: Q5514010
cites work: Finite dimensional translational invariant subspaces
cites work: Q5800952
cites work: On characterizations of exponential polynomials
cites work: CONTINUOUS FUNCTIONS SATISFYING LINEAR RECURRENCE RELATIONS
cites work: Théorie générale des fonctions moyenne-périodiques
cites work: Note on exponential polynomials
cites work: Almost periodicity and functional equations
cites work: Q3744670
cites work: Q3721156
OpenAlex ID: W2021005054
description: scientific article; zbMATH DE number 4124296