Geodesic
On the Fourier coefficients of functions of bounded variation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2013), pp. 14-23 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Olevskii A. M., “Ob ortogonalnykh ryadakh po polnym sistemam”, Matem. sb., 58(100):2 (1962), 707–748 | MR | Zbl

[2] Ulyanov P. L., “O ryadakh po sisteme Khaara”, Matem. sb., 63(105):3 (1964), 356–391 | MR | Zbl

[3] Tsagareishvili V., “On the Fourier coefficients for general orthonormal systems”, Proc. A. Razmadze Math. Inst., 124, 2000, 131–150 | MR | Zbl

[4] Fine N. J., “On the Walsh functions”, Trans. Amer. Math. Soc., 65 (1949), 372–414 | DOI | MR | Zbl

[5] Aleksich G., Problemy skhodimosti ortogonalnykh ryadov, In. lit., M., 1963 | MR

[6] Golubov B. I., Efimov A. V., Skvortsov V. A., Ryady i preobrazovaniya Uolsha, Nauka, M., 1987 | MR | Zbl

[7] Bari N. K., Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR