IJPAM: Volume 89, No. 4 (2013)

THE HANKEL TRANSFORM OF $\delta ^{\left( \nu \right) }\left(x-a\right) $ AND
DISTRIBUTIONAL PRODUCT OF $\delta ^{\left( m\right) }\left(x-a\right) .\delta ^{\left( l\right) }\left( x-b\right) $

Manuel A. Aguirre$^1$, Emilio A. Aguirre$^2$
$^{1,2}$Núcleo Consolidado de Matemática Pura y Aplicada
Facultad de Ciencias Exactas
Universidad Nacional del Centro de la Provincia de Buenos Aires
Tandil, Provincia de Buenos Aires, ARGENTINA

Abstract. One of the problem in distributions theory is the lack of definitions for products and power of distributions in general. In Physics (c.f. [5], p. 141), oneself finds the need to evaluate $\delta ^{2}$ when calculating the transition rates of certain particle interactions. Chankuan Li ([4]) derives that $\delta ^{2}\left( x\right) =0$ on even-dimension space by applying the Laurent expansion of $r=i$. Koh and Li in ([6]) give a sense to distribution $\delta ^{k}$ and $\left( \delta ^{\prime }\right)
^{k} $ for some $k$, using the concept of neutrix limit. In this paper, using the Hankel Transform of Generalized function of $\delta ^{\left(
m\right) }\left( x-a\right) $, we give a sense to distributional product of ^( m) ( x-a) .^( l)

Received: May 28, 2013

AMS Subject Classification:

Key Words and Phrases: distributional product, Dirac delta, propieties of distributions

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DOI: 10.12732/ijpam.v89i4.2 How to cite this paper?
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 4