Vol. 32, No. 2, 1970

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Finite dimensional translation invariant subspaces

Martin Engert

Vol. 32 (1970), No. 2, 333–343

It is known that every finite dimensional translation invariant subspace of the continuous functions on the real line consists of exponential polynomials. The purpose of this paper is to prove an analogous result under the hypotheses that the functions involved are measurable instead of continuous (and two functions are considered identical if they are equal almost everywhere) and that the functions are defined on a σ-compact locally compact abelian group. There is an application of this theorem to the characterization of differential operators at the end of the paper.

Mathematical Subject Classification
Primary: 22.65
Received: 20 December 1968
Published: 1 February 1970
Martin Engert