IJPAM: Volume 71, No. 1 (2011)
RELATED TO THE KLEIN-GORDON OPERATOR
Department of Mathematics
Khon Kaen University
Khon Kaen, 40002, THAILAND
Abstract. In this paper, we study the distribution , where is the Klein-Gordon operator iterated times defined by (), is a non-negative integer, is the Dirac-delta distribution, is a non-negative real number, is a variable and is a constant and both are the points in the -dimensional Euclidean spaces .
At first, the properties of
are studied and after that we study the application of
for solving the solution
of the convolution equation
where is the generalized function and is a constant. It found that the type of solutions of this convolution equation, such as the ordinary function and the singular distribution depend on the relationship between the values of and .
Received: May 5, 2011
AMS Subject Classification: 46F10, 46F12
Key Words and Phrases: convolution equation, tempered distribution, Klein-Gordon operator, Dirac-delta distribution
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395