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Fourier series question
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TCL
Sep 1, 2010, 9:30:08 AM9/1/10
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Does there exist a nonzero (i.e. not equal to 0 a.e.) Lebesgue
integrable function on [0, 2pi] whose Fourier series is 0, i.e. all
its Fourier coefficients are 0 ?
integrable function on [0, 2pi] whose Fourier series is 0, i.e. all
its Fourier coefficients are 0 ?
I don't think the famous Kolmogorov's example answers this question.
Peter Scheffler
Sep 1, 2010, 1:24:51 PM9/1/10
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TCL schrieb:
NO. If \hat f(n)=0 for all integers n then f=0 Lebesgue almost
everywhere (Uniqueness Theorem)
Peter
p.s. didn't you post this on sci.math a few days ago????
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