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487Re: [harmonic] convolutions of restrictions of functions

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  • shravan kumar
    Mar 28, 2011
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      It is better to read Reiter's book on "Classical harmonic analysis and locally compact groups" which contains details on this.

      Shravan

      --- On Tue, 22/2/11, lakshanyamath <lakshanyamath@...> wrote:

      From: lakshanyamath <lakshanyamath@...>
      Subject: [harmonic] convolutions of restrictions of functions
      To: harmonicanalysis@yahoogroups.com
      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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