# IJPAM: Volume 53, No. 2 (2009)

**FORMULAE RELATIONSHIP TO THE DISTRIBUTIONAL**

PRODUCT OF AND

PRODUCT OF AND

Núcleo Consolidado Matemática Pura y Aplicada

Facultad de Ciencias Exactas

Universidad Nacional del Centro

Tandil, Provincia de Buenos Aires, ARGENTINA

e-mail: maguirre@exa.unicen.edu.ar

**Abstract.**One of the problem in distribution theory is the lack of definitions for
products and power of distributions in general. In physics (c.f. [#!Ga!#], p. 141), oneself finds the need to evaluate when calculating
the transition rates of certain particle interactions. Chenkuan Li (see [#!L!#])
derives that
on even-dimension space by applying the
Laurent expansion of . Koh and Li in [#!K!#] give a sense to
distribution and
for some , using the
concept of neutrix limit. Aguirre in [#!A!#], gives a sense to
distributional product of
, using the
Hankel transform of generalized function of
. In this paper
using the Fourier transform of
we obtain formulae for
the distributional product of
and
where and . As
consequence we give a sense at the following product:
and
. Finally, we write formulae relations with
distributional products of
and
where
is
defined by ().

**Received: **March 31, 2009

**AMS Subject Classification: **47Bxx, 45P05, 47G10, 32A25, 32M15

**Key Words and Phrases: **distribution theory, Laurent expansion, Hankel transform

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2009

**Volume:** 53

**Issue:** 2