487Re: [harmonic] convolutions of restrictions of functions
- Mar 28, 2011
It is better to read Reiter's book on "Classical harmonic analysis and locally compact groups" which contains details on this.
--- On Tue, 22/2/11, lakshanyamath <lakshanyamath@...> wrote:
From: lakshanyamath <lakshanyamath@...>
Subject: [harmonic] convolutions of restrictions of functions
Date: Tuesday, 22 February, 2011, 10:07 PM
It would be very helpful for me if anyone could explain the following:
Let G be a locally compact abelian group and H, a closed subgroup of G. Let f,g be integrable functions on G. Then the convolution of the restrictions of f and g to H, and (f * g) restricted to H, are both integrable functions on H(where f * g is the usual convolution of f and g).
Is there any relation between these two functions on H, or between their Fourier transforms?
If not in general, atleast when H is an open subgroup.
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