From: israel@math.ubc.ca (Robert Israel)
Newsgroups: sci.math
Subject: Re: Multiplying distributions
Date: 25 Nov 1998 18:37:11 GMT

In article <gadde-2511981321020001@mac93.sm.luth.se>, gadde@sm.luth.se (Erland Gadde) writes:
|> The product of two distributions K and L is in general not defined,
|> and such a general definition can hardly be given if it should have
|> reasonable properties.
...
|> I wonder if there is any general definition, yielding nice properties,
|> of which these two examples (and possibly others) are special cases. 
|> I mean a definition of the type:
...

Look in Reed and Simon, Methods of Modern Mathematical Physics II: Fourier
Analysis, Self-Adjointness, Academic Press 1975, section IX.10.  Basically
the idea is that (after localizing by multiplying by a test function of
compact support) you want the convolution of the Fourier transforms to
converge absolutely.

Robert Israel                                israel@math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            
Vancouver, BC, Canada V6T 1Z2