International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 324821, 21 pages
http://dx.doi.org/10.1155/2011/324821
Research Article

Restricted Algebras on Inverse Semigroups—Part II: Positive Definite Functions

Massoud Amini1 and Alireza Medghalchi2

1Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O.Box Tehran 14115-134, Iran
2Faculty of Mathematical Sciences and Computer, Tarbiat Moalem University, 50 Taleghani Avenue, Tehran 15614, Iran

Received 13 December 2010; Revised 23 April 2011; Accepted 22 June 2011

Academic Editor: Naseer Shahzad

Copyright © 2011 Massoud Amini and Alireza Medghalchi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. In this paper, we investigate the concept of restricted positive definite functions and their relation with restricted representations of an inverse semigroup. We also introduce the restricted Fourier and Fourier-Stieltjes algebras of an inverse semigroup and study their relation with the corresponding algebras on the associated groupoid.