IJPAM: Volume 71, No. 1 (2011)
ON THE CONVOLUTION EQUATION
RELATED TO THE KLEIN-GORDON OPERATOR
RELATED TO THE KLEIN-GORDON OPERATOR
Amphon Liangprom
, Kamsing Nonlaopon
Department of Mathematics
Khon Kaen University
Khon Kaen, 40002, THAILAND


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




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
Year: 2011
Volume: 71
Issue: 1