IJPAM: Volume 72, No. 2 (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-khin čin formula. Finally, as an application we give the Lévy-khinčin formula for negative definite functions defined on Jacobi polynomial hypergroups.

Received: July 27, 2011

AMS Subject Classification: 43A62, 43A22

Key Words and Phrases: hypergroup, strongly negative definite

Download paper from here.


Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 72
Issue: 2