Dales, H.G. and Millington, A.
(1993)
*Translation-invariant linear operators.*
Mathematical Proceedings of the Cambridge Philosophical Society, 113 (1).
pp. 191-172.
ISSN 0305-0041

## Abstract

The theory of translation-invariant operators on various spaces of functions (or measures or distributions) is a well-trodden field. The problem is to decide, first, whether or not a linear operator between two function spaces on, say, xs211D or xs211D+ which commutes with one or many translations on the two spaces is necessarily continuous, and, second, to give a canonical form for all such continuous operators. In some cases each such operator is zero. The second problem is essentially the ‘multiplier problem’, and it has been extensively discussed; see [7], for example.