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Bochner's Theorem and the Hausdorff Moment Theorem on foundation Topological Semigroups

Published online by Cambridge University Press:  20 November 2018

M. Lashkarizadeh Bami
M. Lashkarizadeh Bami*
Affiliation:
University of Isfahan, Isfahan, Iran
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One of the most basic theorems in harmonic analysis on locally compact commutative groups is Bochner's theorem (see [16, p. 19]). This theorem characterizes the positive definite functions. In 1971, R. Lindhal and P. H. Maserick proved a version of Bochner's theorem for discrete commutative semigroups with identity and with an involution * (see [13]). Later, in 1980, C. Berg and P. H. Maserick in [6] generalized this theorem for exponentially bounded positive definite functions on discrete commutative semigroups with identity and with an involution *. In this work we develop these results, and also the Hausdorff moment theorem, for an extensive class of topological semigroups, the so-called “foundation topological semigroups”. We shall give examples to show that these theorems do not extend in the obvious way to general locally compact topological semigroups.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 5 , 01 October 1985 , pp. 785 - 809
Copyright
Copyright © Canadian Mathematical Society 1985

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