IJPAM: Volume 72, No. 1 (2011)
Department of Mathematics and Computer Science
Brandon, Manitoba, R7A 6A9, CANADA
Abstract. For any Schwartz testing function , the distribution focused on the sphere of in is defined by
which is the solution of the wave equation with the initial conditions described below in a space of odd dimension:
We apply the well-known Pizzetti's formula
to derive an asymptotic expansion for the distribution and obtain an asymptotic product for based on the formula
This product should have potential applications in seeking certain solutions for the differential equations involving the gradient operator in distributional sense.
Received: July 1, 2011
AMS Subject Classification: 46F10
Key Words and Phrases: distribution, product, asymptotic expansion, asymptotic product, wave equation and Pizzetti's formula
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395