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Generalized translations associated with an unbounded self-adjoint operator

Published online by Cambridge University Press:  24 October 2008

B. Fishel
B. Fishel
Affiliation:
Department of Mathematical Sciences, Queen Mary College, London, E1 4NS
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Extract

Delsarte [2], Povzner [9], Levitan [8], Leblanc [7], Dunford and Schwartz [3] (p. 1626) and Hutson and Pym [5] have discussed generalized translation operators (GTO) ‘associating with a differential operator’. The latter authors have also considered the topic in an abstract setting-the GTO ‘associates’ with a compact operator in a normed space. GTO are to have properties generalizing those of the translation operators defined by members of a group on a vector space E of functions defined on the group:

(πεE, s and t are group elements). In the case of a locally compact topological group the integration spaces E = L1,L2,L∞, for a Haar measure of the group, are of especial interest.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 3 , May 1986 , pp. 519 - 528
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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