This article is cited in 3 papers

Salem's Conditions in the Nonperiodic Case

E. R. Liflyand<sup>ab

a</sup> Bar-Ilan University, Ramat Gan
^b Nikol'skii Mathematical Institute of Peoples’ Friendship University of Russia

Abstract: Salem's necessary conditions for a trigonometric series to be the Fourier series of an integrable function are generalized to the nonperiodic case for functions in the Wiener algebra. Applications of the obtained result are given.

Keywords: Wiener algebra, trigonometric series, discrete Hilbert transform, modified Hilbert transform, Fourier transform.

UDC: 517.518.5

Received: 30.11.2017
Revised: 02.03.2018

DOI: 10.4213/mzm12116

 English version: Mathematical Notes, 2018, 104:3, 437–442

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