Abstract and Applied Analysis
Volume 2011, Article ID 908491, 16 pages
http://dx.doi.org/10.1155/2011/908491
On the Convolution Equation Related to the Diamond Klein-Gordon Operator
1Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
Received 11 July 2011; Revised 3 August 2011; Accepted 31 August 2011
Academic Editor: Elena Braverman
Copyright © 2011 Amphon Liangprom and Kamsing Nonlaopon. 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 study the distribution for , where is the diamond Klein-Gordon operator iterated times, is the Dirac delta distribution, is a variable in , and is a constant. In particular, we study the application of for solving the solution of some convolution equation. We find that the types of solution of such convolution equation, such as the ordinary function and the singular distribution, depend on the relationship between and .