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Translation-invariant linear operators

Published online by Cambridge University Press:  24 October 2008

H. G. Dales  and
A. Millinoton
H. G. Dales
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT
A. Millinoton
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT
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Extract

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, ℝ or ℝ+ 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 1 , January 1993 , pp. 161 - 172
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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