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Representations and positive definite functions on topological semigroups

Published online by Cambridge University Press:  18 May 2009

J. W. Baker  and
M. Lashkarizadeh-Bami
J. W. Baker
Affiliation:
Department of Pure Mathematics, The University, Sheffield S3 7RH, England, U.K.
M. Lashkarizadeh-Bami
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan, Iran
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Abstract

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A number of theorems are established about positive definite functions and representations of certain topological semigroups. In particular we establish theorems which show that measurable positive definite functions and measurable representations can each be decomposed into the sum of two parts one of which is continuous and the other of which is “small”.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 1 , January 1996 , pp. 99 - 111
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

1.Baker, A. C. and Baker, J. W., Algebras of measures on a locally compact semigroup II, J. London Math. Soc. 2 (1970), 651–659.CrossRefGoogle Scholar
2.Baker, J. W. and Lashkarizadeh-Bami, M., On the representations of certain idempotent topological semigroups, Semigroup Forum 44 (1992), 245–254.CrossRefGoogle Scholar
3.Berg, C., Christensen, J. P. R. and Ressel, P., Harmonic analysis on semigroups (Springer-Verlag, New York, 1984).CrossRefGoogle Scholar
4.Dzinotyiweyi, H. A. M., The analogue of the group algebra for topological semigroups (Pitman, 1984).Google Scholar
5.Hofmann, K. H., Lawson, J. D. and Pym, J. S., The analytical and topological theory of semigroups (de Gruyter, 1990).CrossRefGoogle Scholar
6.Hewitt, E. and Ross, K. A., Abstract harmonic analysis, I (Springer-Verlag, 1963).Google Scholar
7.Hewitt, E. and Ross, K. A., Abstract harmonic analysis, II (Springer-Verlag, 1970).Google Scholar
8.Lashkarizadeh-Bami, M., Representations of foundation semigroups and their algebras, Canadian J. Math. 37 (1985), 29–47.CrossRefGoogle Scholar
9.Lashkarizadeh-Bami, M., Bochner's theorem and the Hausdorff moment theorem on foundation semigroups, Canadian J. Math. 37 (1985), 785–809.CrossRefGoogle Scholar
10.Lashkarizadeh-Bami, M., On various types of convergence of positive-definite functions on foundation semigroups, Math. Proc. Camb. Phil. Soc. 111 (1992), 325–330.CrossRefGoogle Scholar
11.Simmons, G. F., Introduction to topology and modern analysis (McGraw-Hill, 1963).Google Scholar