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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Compactly bounded convolutions of measures


Author: Adam W. Parr
Journal: Proc. Amer. Math. Soc. 130 (2002), 2661-2667
MSC (2000): Primary 43A99
Published electronically: March 13, 2002
MathSciNet review: 1900874
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Abstract: In this paper we extend classical results concerning generalized convolution structures on measure spaces. Given a locally compact Hausdorff space $X$, we show that a compactly bounded convolution of point masses that is continuous in the topology of weak convergence with respect to $C_{c}(X)$ can be extended to a general convolution of measures which is separately continuous in the topology of weak convergence with respect to $C_{b}(X)$.


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Additional Information

Adam W. Parr
Affiliation: Department of Mathematics, University of the Virgin Islands, St. Thomas, United States Virgin Islands
Email: aparr@uvi.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06513-9
PII: S 0002-9939(02)06513-9
Keywords: Signed hypergroup, convolution, strict topology
Received by editor(s): April 6, 2001
Published electronically: March 13, 2002
Communicated by: Andreas Seeger
Article copyright: © Copyright 2002 American Mathematical Society