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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 8, Pages 14–23 (Mi ivm8814)  
On the Fourier coefficients of functions of bounded variation

L. D. Gogoladze, V. Sh. Tsagareishvili

Department of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University, 1 I. Chavchavadze Ave., Tbilisi, 0128 Georgia
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Abstract: 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, Fourier coefficients, trigonometric system, Walsh system, Haar system.
Received: 06.04.2012
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, Volume 57, Issue 8, Pages 10–19
DOI: https://doi.org/10.3103/S1066369X13080021
Bibliographic databases:
Document Type: Article
UDC: 517.521
Language: Russian
Citation: L. D. Gogoladze, V. Sh. Tsagareishvili, “On the Fourier coefficients of functions of bounded variation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 8, 14–23; Russian Math. (Iz. VUZ), 57:8 (2013), 10–19
Citation in format AMSBIB
\Bibitem{GogTsa13}
\by L.~D.~Gogoladze, V.~Sh.~Tsagareishvili
\paper On the Fourier coefficients of functions of bounded variation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 8
\pages 14--23
\mathnet{http://mi.mathnet.ru/ivm8814}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 8
\pages 10--19
\crossref{https://doi.org/10.3103/S1066369X13080021}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84881351521}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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