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The Fourier coefficients of functions with bounded variation

Abstract

We consider Fourier coefficients for functions of bounded variation with respect to general orthonormal systems (GONS). We show that in general case the sequence of coefficients may have an arbitrarily prescribed order of vanishing. In this connection we seek for a class of GONS such that Fourier coefficients of a function from V(0, 1) satisfy the same inequality as in the case of classical systems (trigonometric, Walsh, and Haar ones). In the present paper we study this problem and related issues.

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Correspondence to L. D. Gogoladze.

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Original Russian Text © L.D. Gogoladze and V.Sh. Tsagareishvili, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 8, pp. 14–23.

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Gogoladze, L.D., Tsagareishvili, V.S. The Fourier coefficients of functions with bounded variation. Russ Math. 57, 10–19 (2013). https://doi.org/10.3103/S1066369X13080021

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  • DOI: https://doi.org/10.3103/S1066369X13080021

Keywords and phrases

  • Fourier series
  • Fourier coefficients
  • trigonometric system
  • Walsh system
  • Haar system