The associated measure on locally compact cocommutative KPC-hypergroups

Document Type : Research Paper

Authors

1 Department of Mathematics‎, ‎The University of Qom‎, ‎3716146611‎, ‎Iran.

2 Department of Mathematics‎, ‎The University of Qom‎, ‎371614\newline 6611‎, ‎Iran.

Abstract

We study harmonic analysis on cocommutative KPC-hyper-groups‎, which is a generalization of DJS-hypergroups‎, ‎introduced by Kalyuzhnyi‎, ‎Podkolzin and Chapovsky‎. ‎We prove that there is a relationship between‎ ‎the associated measures $\mu$ and $\gamma \mu$‎, ‎where $\mu$ is‎ ‎a Radon measure on KPC-hypergroup $Q$ and $\gamma$ is a character on $Q$.

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References

W. R. Bloom and H. Heyer, Harmonic Analysis of Probability Measures on Hypergroups, Walter de Gruyter, Berlin, 1995.
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R. I. Jewett, Spaces with an abstract convolution of measures, Adv. Math. 18 (1975), no. 1, 1--101.
A. A. Kalyuzhnyi, G. B. Podkolzin and Y. A. Chapovski, Harmonic analysis on a locally compact hypergroup, Methods Funct. Anal. Topology 16 (2010), no. 4, 304--332.
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R. Spector, Measures invariantes sur les hypergroupes, Trans. Amer. Math. Soc. 239 (1978) 147--165.
Bulletin of the Iranian Mathematical Society
Volume 43, Issue 1
February 2017
Pages 1-15

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History

  • Receive Date: 08 February 2015
  • Revise Date: 23 September 2015
  • Accept Date: 03 October 2015

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