In this article, we consider the equation
where is the operator iterated k times and defined by
where , is in the n-dimensional Euclidian space , is a constant, is the Dirac-delta 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: Ultra-hyperbolic kernel; diamond operator; tempered distribution.
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| Wanchak Satsanit |
Department of Mathematics
Faculty of Science, Maejo University
Chiang Mai, 50290 Thailand
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