Vol. 16, No. 2, 1966

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Operators commuting with translations

Robert E. Edwards

Vol. 16 (1966), No. 2, 259–265

This paper is concerned with the representation, in terms of convolutions with pseudomeasures, of continuous linear operators which commute with translations and which transform continuous functions with compact supports on a Hausdorff locally compact Abelian group G into restricted types of Radon measures on G. The two main theorems each assert that any such operator T is of the form Tf = s f for a suitably chosen pseudomeasure s on G; the assertions differ in detail in respect of the hypotheses imposed on the range of T. The second theorem is an extension of Proposition 2 of [1] from the case in which G is a finite product of lines and/or circles to the general situation.

Mathematical Subject Classification
Primary: 42.50
Received: 15 October 1964
Published: 1 February 1966
Robert E. Edwards