- 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.Final published version, 778 KB, PDF document

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**Translation-invariant linear operators.** / Dales, H.G.; Millington, A.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Dales, HG & Millington, A 1993, 'Translation-invariant linear operators', *Mathematical Proceedings of the Cambridge Philosophical Society*, vol. 113, no. 1, pp. 191-172. https://doi.org/10.1017/S030500410007585X

Dales, H. G., & Millington, A. (1993). Translation-invariant linear operators. *Mathematical Proceedings of the Cambridge Philosophical Society*, *113*(1), 191-172. https://doi.org/10.1017/S030500410007585X

Dales HG, Millington A. Translation-invariant linear operators. Mathematical Proceedings of the Cambridge Philosophical Society. 1993 Jan;113(1):191-172. doi: 10.1017/S030500410007585X

@article{7015a97bbb6c4de7bee201b5cea5983b,

title = "Translation-invariant linear operators",

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 {\textquoteleft}multiplier problem{\textquoteright}, and it has been extensively discussed; see [7], for example.",

author = "H.G. Dales and A. Millington",

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, {\textcopyright} 1993 Cambridge University Press.",

year = "1993",

month = jan,

doi = "10.1017/S030500410007585X",

language = "English",

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AU - Dales, H.G.

AU - Millington, A.

N1 - 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.

PY - 1993/1

Y1 - 1993/1

N2 - 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.

AB - 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.

U2 - 10.1017/S030500410007585X

DO - 10.1017/S030500410007585X

M3 - Journal article

VL - 113

SP - 191

EP - 172

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 1

ER -