International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 352590, 10 pages
http://dx.doi.org/10.1155/2011/352590
Research Article

Garding's Inequality for Elliptic Differential Operator with Infinite Number of Variables

Ahmed Zabel1 and Maryam Alghamdi2

1Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, 11884 Cairo, Egypt
2Department of Mathematics, King Abdulaziz University, P.O. Box 4087, Jeddah 21491, Saudi Arabia

Received 21 July 2010; Accepted 17 November 2010

Academic Editor: Zayid Abdulhadi

Copyright © 2011 Ahmed Zabel and Maryam Alghamdi. 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

We formulate the elliptic differential operator with infinite number of variables and investigate that it is well defined on infinite tensor product of spaces of square integrable functions. Under suitable conditions, we prove Garding's inequality for this operator.