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On Theorems of Kawada and Wendel

Published online by Cambridge University Press:  20 January 2009

J. H. Williamson
J. H. Williamson
Affiliation:
The Queen's University, Belfast
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Let G be a locally compact topological group, with left-invariant Haar measure. If L1(G) is the usual class of complex functions which are integrable with respect to this measure, and μ is any bounded Borel measure on G, then the convolution-product μ⋆f, defined for any f in Li by

is again in L1, and

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 11 , Issue 2 , November 1958 , pp. 71 - 77
Copyright
Copyright © Edinburgh Mathematical Society 1958

References

REFERENCES

(1) Kawada, Y., On the group ring of a topological group, Math. Jap., 1 (1948), 1–5.Google Scholar
(2) Loomis, L. H., Abstract Harmonic Analysis (van Nostrand, New York, 1953).Google Scholar
(3) Wendel, J. G., Left centralizers and isomorphisms of group algebras, Pacific J. Math., 2 (1952), 251–61.CrossRefGoogle Scholar