Regularity properties of polynomials on groups
type: Item
instance of: scholarly article
title: Regularity properties of polynomials on groups
zbMATH Open document ID: 0578.39004
DOI: 10.1007/BF01955017
published in: Acta Mathematica Hungarica
publication date: 1985-01-01T00:00:00Z
review text: The author is concerned with regularity properties of polynomials on groups. His results can be used to characterize regular solutions of general linear functional equations on commutative topological groups and also extend some classical results concerning the Cauchy-, Pexider-, Fréchet-, and square-norm-equations. One of the main results proved in this paper is as follows: Theorem. Let G be a locally compact abelian group which is generated by any neighborhood of the zero and let X be a locally convex and locally bounded topological linear space. If a polynomial \(p: G\to X\) is measurable on a measurable set of positive measure, then it is continuous.
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 43A70
zbMATH DE Number: 3925439
zbMATH Keywords: regularity properties
zbMATH Keywords: polynomials
zbMATH Keywords: linear functional equations
zbMATH Keywords: commutative topological groups
zbMATH Keywords: Cauchy
zbMATH Keywords: Pexider
zbMATH Keywords: Fréchet
zbMATH Keywords: locally convex
zbMATH Keywords: locally bounded
zbMATH Keywords: measurable set of positive measure
zbMATH Keywords: continuous
author: László Székelyhidi
reviewed by: Hiroshi Haruki
MaRDI profile type: Publication
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cites work: Boundedness on a set of positive measure and the mean value property characterizes polynomials on a space \(V^ n\)
cites work: Q4746204
full work available at URL: https://doi.org/10.1007/bf01955017
OpenAlex ID: W2057976098
description: scientific article; zbMATH DE number 3925439