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1 vote

Error of Discrete Fourier Transform on Finite Domain (vs. Continuous FT) in terms of Sobolev...

Also note a paper, but it is in Russian: Kurbatov A.V., Kurbatov V.G. Approximation of (integral) FT via DFT. http://www.vestnik.vsu.ru/program/view/view.asp?sec=physmath&year=2012&num=02&f_name=2012 …
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8 votes

Positivity of certain Fourier transform

This is a well-known problem, solved recently in dissertation of Zastavny based on some inequalities for p.d.f. More: it is a Schonberg problem, positive for $0<m\leq1$, not positive otherwise.
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