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

  • $\begingroup$ google.com/… $\endgroup$ Commented Mar 22, 2010 at 8:58
  • $\begingroup$ Do none of those articles answer your question? $\endgroup$ Commented Mar 22, 2010 at 8:59
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    $\begingroup$ 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. $\endgroup$ Commented Mar 22, 2010 at 14:01
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    $\begingroup$ It's remarkable how quickly this question went to the top of the results for that search (at least on my computer). $\endgroup$ Commented Mar 22, 2010 at 16:21
  • $\begingroup$ Most of the Tulone and Skvortsov stuff seems to be for zero-dimensional LC groups. $\endgroup$ Commented Mar 29, 2010 at 4:03


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