On the distribution related to the ultra-hyperbolic equations

✍ Scribed by Amnuay Kananthai

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 279 KB
• Volume: 84
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(97)00114-3

✦ Synopsis

In this paper we consider the distribution e ~' Dk6 where ~ is a constant and ~ = (~1,~2,...,~,)E R n the n-dimensional Euclidean space and the variable t = (h,t2,...,t,)E ~" and D k is the n-dimensional ultra-hyperbolic operator iterated k-times, 6 is the Dirac-delta distribution with D°6 = 6 and [5]~6 = []6.

At first, all properties of e ~t i-]k6 are studied and after that we study the application of e ~t []k6 for solving the elementary solution of the equation of the ultra-hyperbolic type by using the convolution method.