Note on exponential polynomials

László Székelyhidi

Vol. 103 (1982), No. 2, 583–587

DOI: 10.2140/pjm.1982.103.583

Abstract

It is known that every finite dimensional translation invariant subspace of measurable functions on a σ-compact locally compact Abelian group consists of exponential polynomials. This paper extends this result for continuous functions on arbitrary commutative topological groups. An analogous characterization is proved for trigonometric polynomials using Fourier transformation.

Mathematical Subject Classification 2000

Primary: 43A15

Secondary: 22A10, 22D10, 43A60, 43A65

Milestones

Received: 28 January 1980

Published: 1 December 1982