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Abstract harmonic analysis of generalised functions on locally compact semigroups with applications to invariant means

Published online by Cambridge University Press:  09 April 2009

James C. S. Wong
James C. S. Wong
Affiliation:
Department of Mathematics and Statistics, The University of Calgary, Canada, T2N IN4.
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Abstract

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Let S be a locally compact semigroup and M(S) its measure algebra. It is shown that the dual M(S)* is isometrically order isomorphic to the space GL(S) of all generalised functions on S first introduced by Šreǐder (1950). Moreover, convolutions of elements in each of the spaces M(S)* and GL(S) can be defined in such a way that the above isomorphism preserves convolutions. These results on representation of functionals in M(S)* by generalised functions practically open up a new chapter in abstract harmonic analysis. As an example, some applications to invariant means on locally compact semigroups are given.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1977 , pp. 84 - 94
Copyright
Copyright © Australian Mathematical Society 1977

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