IJPAM: Volume 30, No. 2 (2006)

THE CONVOLUTION PRODUCT OF $n-$DIMENSIONAL
ULTRAHYPERBOLIC OPERATOR OF $(\frac{n}{2}-k-1)$-TH
DERIVATIVE OF DIRAC'S DELTA IN HYPERCONE

Manuel A. Aguirre T.
Núcleo Consolidado Matemática Pura y
Aplicada (NuCOMPA)
Facultad de Ciencias Exactas
Universidad Nacional del Centro
Pinto 399, Tandil, 7000, ARGENTINA
e-mail: maguirre@exa.unicen.edu.ar


Abstract.In this paper we obtain a relation between the distribution $\delta ^{(\frac{% n}{2}-l-1)}(u)$ and the $n$-dimensional ultrahyperbolic operator iterated $% s-times.$ As a consequence we give a sense to convolution distributional product of $L^{s}\left\{ \delta ^{(\frac{n}{2}-k-1)}(u)\right\} \ast L^{t}\left\{ \delta ^{(\frac{n}{2}-l-1)}(u)\right\} .$ Our convolution product result in a generalization of the convolution product $\delta ^{(% \frac{n}{2}-k-1)}(u)\ast \delta ^{(\frac{n}{2}-l-1)}(u)$ due to M. Aguirre T. (c.f. [#!A4!#]).

Received: May 20, 2006

AMS Subject Classification: 46F10, 46F12

Key Words and Phrases: theory of distributions, distributional convolution product

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 2