Vol. 80, No. 2, 1979

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On characterizations of exponential polynomials

Philip G. Laird

Vol. 80 (1979), No. 2, 503–507

This paper considers some characterizations of exponential polynomials in C(G), the set of all continuous complex valued functions on a σ-compact locally compact Abelian group G. For f C(G), Uf will denote the subspace of C(G) obtained by taking finite linear combinations of translates of f. It is known that f is an exponential polynomial if and only if Uf is of finite dimension. Our main result is to show that f is an exponential polynomial when Uf is closed in C(G) if C(G) is given the topology of convergence uniform on all compact subsets of G.

Further characterizations of exponential polynomials are given when G is real Euclidean n-space, Rn.

Mathematical Subject Classification 2000
Primary: 43A15
Received: 4 January 1977
Revised: 12 July 1978
Published: 1 February 1979
Philip G. Laird