Translation-invariant linear operators

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

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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.

Item Type: Journal Article
Journal or Publication Title: Mathematical Proceedings of the Cambridge Philosophical Society
Additional Information: 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.
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2600
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 67614
Deposited By: ep_importer_pure
Deposited On: 20 Nov 2013 11:59
Refereed?: Yes
Published?: Published
Last Modified: 19 Oct 2019 00:02
URI: https://eprints.lancs.ac.uk/id/eprint/67614

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