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  • S030500410007585Xa

    Rights statement: http://journals.cambridge.org/action/displayJournal?jid=PSP The final, definitive version of this article has been published in the Journal, Mathematical Proceedings of the Cambridge Philosophical Society, 113 (1), pp 161-172 1993, © 1993 Cambridge University Press.

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Translation-invariant linear operators

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>01/1993
<mark>Journal</mark>Mathematical Proceedings of the Cambridge Philosophical Society
Issue number1
Volume113
Number of pages12
Pages (from-to)191-172
<mark>State</mark>Published
<mark>Original language</mark>English

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.

Bibliographic note

http://journals.cambridge.org/action/displayJournal?jid=PSP The final, definitive version of this article has been published in the Journal, Mathematical Proceedings of the Cambridge Philosophical Society, 113 (1), pp 161-172 1993, © 1993 Cambridge University Press.