Geodesic
The Fourier Coefficients of Continuous Functions with Respect to Certain Orthonormal Systems
Matematičeskie zametki, Tome 99 (2016) no. 3, pp. 428-440.

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

The properties of the Fourier coefficients for some classes of functions with respect to both the Haar system and general orthonormal systems are studied. It is established that the results obtained in the paper cannot be strengthened.
Mots-clés : Fourier coefficient
Keywords: orthonormal system, Haar system, Rademacher function, modulus of continuity, Bessel's inequality. 
@article{MZM_2016_99_3_a12,
     author = {V. Sh. Tsagareishvili},
     title = {The {Fourier} {Coefficients} of {Continuous} {Functions} with {Respect} to {Certain} {Orthonormal} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {428--440},
     publisher = {mathdoc},
     volume = {99},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_3_a12/}
}
TY  - JOUR
AU  - V. Sh. Tsagareishvili
TI  - The Fourier Coefficients of Continuous Functions with Respect to Certain Orthonormal Systems
JO  - Matematičeskie zametki
PY  - 2016
SP  - 428
EP  - 440
VL  - 99
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_99_3_a12/
LA  - ru
ID  - MZM_2016_99_3_a12
ER  - 
%0 Journal Article
%A V. Sh. Tsagareishvili
%T The Fourier Coefficients of Continuous Functions with Respect to Certain Orthonormal Systems
%J Matematičeskie zametki
%D 2016
%P 428-440
%V 99
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2016_99_3_a12/
%G ru
%F MZM_2016_99_3_a12
V. Sh. Tsagareishvili. The Fourier Coefficients of Continuous Functions with Respect to Certain Orthonormal Systems. Matematičeskie zametki, Tome 99 (2016) no. 3, pp. 428-440. http://geodesic.mathdoc.fr/item/MZM_2016_99_3_a12/

[1] B. C. Kashin, A. A. Saakyan, Ortogonalnye ryady, Izd-vo AFTs, M., 1999 | MR | Zbl

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

[3] V. Sh. Tsagareishvili, “O variatsii koeffitsientov Fure–Khaara”, Matem. sb., 195:3 (2004), 143–160 | DOI | MR | Zbl

[4] V. Tsagareishvili, “Fourier–Haar coefficients of continuous functions”, Acta Math. Hugar., 132:1-2 (2011), 1–14 | DOI | MR | Zbl

[5] G. Aleksich, Problemy skhodimosti ortogonalnykh ryadov, IL, M., 1963 | MR | Zbl

[6] A. F. Timan, Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatlit, M., 1960 | MR

[7] S. Banach, “Sur la divergence des séries orthogonales”, Studia Math., 9 (1940), 139–155 | MR | Zbl

[8] V. Sh. Tsagareishvili, “Absolyutnaya skhodimost ryadov Fure funktsii iz klassa $\operatorname{Lip}1$ i funktsii ogranichennoi variatsii”, Izv. RAN. Ser. matem., 76:2 (2012), 215–224 | DOI | MR | Zbl

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