Geodesic
On the Fourier coefficients of functions of bounded variation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2013), pp. 14-23

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We notice that the Fourier coefficients of functions with bounded variation $V(0,1)$ with respect to general orthonormal systems (GONS) have no definite order of vanishing. In this connection we study the problem: which requirements to the GONS ensure that the Fourier coefficients of a function from $V(0,1)$ satisfy the inequality which holds for classical systems (trigonometric, Walsh, or Haar ones). In the present paper we study this problem and related issues.
Keywords: Fourier series, trigonometric system, Walsh system, Haar system.
Mots-clés : Fourier coefficients 
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     author = {L. D. Gogoladze and V. Sh. Tsagareishvili},
     title = {On the {Fourier} coefficients of functions of bounded variation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {14--23},
     publisher = {mathdoc},
     number = {8},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_8_a1/}
}
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L. D. Gogoladze; V. Sh. Tsagareishvili. On the Fourier coefficients of functions of bounded variation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2013), pp. 14-23. http://geodesic.mathdoc.fr/item/IVM_2013_8_a1/