A Question About Fourier Series

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1 total messages Started by TAROKH VAHID Mon, 27 Jul 1992 19:02

#22

Author: TAROKH VAHID
Date: Mon, 27 Jul 1992 19:02

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Dear Readers,

Let f denote a continuous function. By Parseval equality, we know that the
Fourier series of ' f ' converges in L^2 to f. It was told to me that a theorem
of Fefferman gives a similar result for L^p , where p>1.  Is this true?  Second
what can be said if p < 1?  Third is there a function f periodic and continuous
whose Fourier series nowhere converges?  Fourth what could be said about
functions of locally compact groups to the real line?  Is there any theory
similar to Fourier series for them?

              Thank You 
              Vahid Tarokh

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