Electron. J. Diff. Equ.,
Vol. 2010(2010), No. 76, pp. 19.
Solutions of a partial differential equation related to the
oplus operator
Wanchak Satsanit
Abstract:
In this article, we consider the equation
where
is the operator iterated k times and
defined by
where
,
is in
the ndimensional Euclidian space
,
is a constant,
is the
Diracdelta distribution,
, and
.
It is shown that, depending on the
relationship between k and m, the solution to this equation
can be ordinary functions, tempered distributions,
or singular distributions.
Submitted April 8, 2010. Published June 8, 2010.
Math Subject Classifications: 46F10, 46F12.
Key Words: Ultrahyperbolic kernel; diamond operator;
tempered distribution.
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Wanchak Satsanit
Department of Mathematics
Faculty of Science, Maejo University
Chiang Mai, 50290 Thailand
email: aunphue@live.com

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