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Results tagged with fourier-analysis
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user 49208
The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.
2
votes
Fourier transform of $sin(\frac{1}{x})$ for $x > 0 (x > 1)$
The explicit answer is the formula 2.5.24.1 on page 433 from Brychkov, Marichev, Prudnikov Integral and Series, vol. 1. Note that for the odd function the FT reduces to sinT, and take $\alpha=1, \delt …
- 1,560
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 …
- 1,560
2
votes
Accepted
A book about almost periodic functions
What do you mean "a new", of what years?
Classics are always new-the books of Bohr, Levitan and Zhikov, Besikovich himself.
There is also a book of Corduneanu with standard name "almost periodic funct …
- 1,560
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.
- 1,560
5
votes
Accepted
Variations on the Mellin and Dirichlet transforms
I know that the discrete Mellin transform was defined by V.S.Ryko:
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ivm&paperid=5138&option_lang=rus
English reference: Soviet Mathematics (Izv …
- 1,560