Journal of Mathematical Sciences

, Volume 244, Issue 1, pp 65–94 | Cite as

On the Fourier series and Fourier transforms

  • Roald M. TrigubEmail author


This survey article is addresses to classical harmonic analysis. In particular, a number of classical theorems are presented with the simplest, in our opinion, proofs (see also [1] and references therein). Some results of the present article are new and are published for the first time.


Theorems by Bernstein Paley–Wiener Levitan and Kotel’nikov–Shannon uncertainty principle Titchmarsh theorem of convolution Whitney theorem Euler–Maclaurin generalized formula Wiener algebra positive definiteness Bessel function 


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Sumy State UniversitySumyUkraine

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