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. / Dales, H.G.; Millington, A.
In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 113, No. 1, 01.1993, p. 191-172.Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Translation-invariant linear operators
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 -