Regularity properties of exponential polynomials on groups (Q1066367)

The author has studied regularity properties of polynomials on groups [ibid. 45, 15-19 (1985; reviewed above)]. The results extend some classical theorems and can be applied in the theory of functional equations. The present paper is concerned with the study of regularity properties of exponential polynomials on Abelian groups. 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 zero, H a locally convex and locally bounded topological vector space, \(f: G\to H\) an exponential polynomial. If f is measurable on some measurable set of positive measure, then it is continuous.