NetNews Usenet Archive 1992 #16/NN_1992_16.iso/spool/sci/math/research/398

Internet Message Format | 1992-07-27 | 1.2 KB

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From: [e-mail] (TAROKH VAHID             )
Newsgroups: sci.math.research
Subject: A Question About Fourier Series
Keywords: L^p convergence of the Fourier Series
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Date: 27 Jul 92 19:02:21 GMT
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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