IJPAM: Volume 71, No. 4 (2011)

ON STRONGLY NEGATIVE DEFINITE FUNCTIONS FOR
THE PRODUCT OF COMMUTATIVE HYPERGROUPS

A.S. Okb El Bab$^1$, Hossam A. Ghany$^2$, S. Ramadan$^3$
$^{1,3}$ Department of Mathematics
Faculty of Science
Al Azhar University
Naser City, Cairo, EGYPT
$^{2}$ Department of Mathematics
Faculty of Industrial Education
Helwan University
Al-Ameraia, Cairo, EGYPT


Abstract. We study strongly negative definite functions on the product dual hypergroups and use their properties to give a proof of the Lévy-khinčin formula. Finally, as an application we give the Lévy-khinčin formula for negative definite functions defined on Jacobi polynomial hypergroups.

Received: April 11, 2011

AMS Subject Classification: 43A62, 43A22

Key Words and Phrases: harmonic analysis, hypergroup, commutative hypergroup, semicharacter, strongly negative definite functions, convolution structure

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 71
Issue: 4