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Is it possible to define Fourier transforms on locally compact commutative groups using the Kurzweil-Henstock integral instead of the Lebesgue integral?

edited Mar 22 2010 at 15:39

Pete L. Clark
39.6k●3●102●226

asked Mar 22 2010 at 8:27

teil
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google.com/… – Harry Gindi Mar 22 2010 at 8:58

Do none of those articles answer your question? – Harry Gindi Mar 22 2010 at 8:59

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The question is essentially, can you use the Haar measure with the K-H integral. My guess is that it is not possible. The whole beauty of the Lebesgue integral is that it can be defined with respect to an arbitrary measure. – Harry Gindi Mar 22 2010 at 14:01

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It's remarkable how quickly this question went to the top of the results for that search (at least on my computer). – Mark Meckes Mar 22 2010 at 16:21

Most of the Tulone and Skvortsov stuff seems to be for zero-dimensional LC groups. – Steve Huntsman Mar 29 2010 at 4:03

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Anil P · Answer 1 · 2011-06-11 16:08:18Z UTC

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it can be done .see treatise of henstock

answered Jun 11 2011 at 16:08

Anil P
33●6

Fourier transforms and the Kurzweil-Henstock integral

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