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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{IVM_2013_8_a1,
     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/}
}
TY  - JOUR
AU  - L. D. Gogoladze
AU  - V. Sh. Tsagareishvili
TI  - On the Fourier coefficients of functions of bounded variation
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 14
EP  - 23
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_8_a1/
LA  - ru
ID  - IVM_2013_8_a1
ER  - 
%0 Journal Article
%A L. D. Gogoladze
%A V. Sh. Tsagareishvili
%T On the Fourier coefficients of functions of bounded variation
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 14-23
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2013_8_a1/
%G ru
%F IVM_2013_8_a1
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