IJPAM: Volume 22, No. 4 (2005)

A NOTE ON THE SOLUTIONS OF
DISTRIBUTIONAL EQUATIONS

Adem Kiliçman
Department of Mathematics
University Putra Malaysia
43400 UPM, Serdang, Selangor Darul Ehsan, MALAYSIA
e-mail: akilic@fsas.upm.edu.my

Abstract.In this study we let ${\cal D}$ be the space of infinitely differentiable functions with compact support and let ${\cal D'}$ be the space of distributions defined on ${\cal D}$ . Then we attempt to solve the distributional equation in the form of

$\begin{displaymath}p\cdot f =g, \end{displaymath}$

where

is a polynomial which has several zeros and

is a given distribution in ${\cal D'}$ and further we prove that $p\cdot f =g$ has distributional solution in ${\cal D'}$ .

Received: February 24, 2005

AMS Subject Classification: 33B10, 46F10

Key Words and Phrases: distributions, delta-function, neutrix, neutrix limit, neutrix product, distributional solutions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 4

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