Regularity properties of polynomials on groups
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.
scientific article; zbMATH DE number 3925439