IJPAM: Volume 64, No. 1 (2010)

HARMONIC ANALYSIS ON HYPERGROUPS

A.S. Okb El Bab$^1$, Hossam A. Ghany$^2$
$^1$Department of Mathematics
Faculty of Science
Al Azhar University
Naser City, Cairo, 11371, EGYPT
e-mail: [email protected]
$^2$Department of Mathematics
Faculty of Industrial Education
Helwan University
Al-Ameraia, Cairo, 11790, EGYPT
e-mail: [email protected]


Abstract.The main task in this article is to give the necessary and sufficient conditions which guarantee that the product of two positive definite functions defined on a hypergroup $X$ is also positive definite on $X$. Also, we prove that a continuous function with compact support $\psi$ is negative definite if and only if $\exp(-t\psi)$ is positive definite for each $t>0$. Moreover, we will give some relations between the class of completely monotonic functions on a hypergroup and the set of $\tau$-positive functions.

Received: September 14, 2009

AMS Subject Classification: 43A62, 43A22, 43A10

Key Words and Phrases: hypergroup, positive definite, completely monotone

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 1