Geodesic
Estimates for the rate of convergence of Fourier series in the Sobolev orthogonal functional system generated by the Walsh system
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 2, Tome 200 (2021), pp. 73-80.

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

For functions from the Sobolev spaces $W^r_{L^p}$, we obtain several estimates for the rate of approximation by partial sums of Fourier series in Sobolev-type system generated by Walsh system: pointwise estimates; uniform estimates in terms of the integral modulus of continuity for the derivative; estimates in the metric of the Sobolev space $W^r_{L^p}$ in terms of the best approximations.
Keywords: Sobolev inner product, Walsh system, approximation properties, Sobolev space, Fourier series. 
@article{INTO_2021_200_a7,
     author = {M. G. Magomed-Kasumov},
     title = {Estimates for the rate of convergence of {Fourier} series in the {Sobolev} orthogonal functional system generated by the {Walsh} system},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {73--80},
     publisher = {mathdoc},
     volume = {200},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_200_a7/}
}
TY  - JOUR
AU  - M. G. Magomed-Kasumov
TI  - Estimates for the rate of convergence of Fourier series in the Sobolev orthogonal functional system generated by the Walsh system
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2021
SP  - 73
EP  - 80
VL  - 200
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2021_200_a7/
LA  - ru
ID  - INTO_2021_200_a7
ER  - 
%0 Journal Article
%A M. G. Magomed-Kasumov
%T Estimates for the rate of convergence of Fourier series in the Sobolev orthogonal functional system generated by the Walsh system
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2021
%P 73-80
%V 200
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2021_200_a7/
%G ru
%F INTO_2021_200_a7
M. G. Magomed-Kasumov. Estimates for the rate of convergence of Fourier series in the Sobolev orthogonal functional system generated by the Walsh system. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 2, Tome 200 (2021), pp. 73-80. http://geodesic.mathdoc.fr/item/INTO_2021_200_a7/

[1] Gadzhimirzaev R. M., “Ryady Fure po polinomam Meiksnera, ortogonalnym po Sobolevu”, Izv. Saratov. un-ta. Nov. ser. Ser. Mat. Mekh. Inform., 16:4 (2016), 388–395 | MR

[2] Golubov B. I., Efimov A. V., Skvortsov V A., Ryady i preobrazovaniya Uolsha: Teoriya i primeneniya, Nauka, M., 1987

[3] Magomed-Kasumov M. G., “Sistema funktsii, ortogonalnaya v smysle Soboleva i porozhdennaya sistemoi Uolsha”, Mat. zametki., 105:4 (2019), 545-–552 | MR | Zbl

[4] Magomed-Kasumov M.G., “Approksimativnye svoistva ryadov Fure po sisteme funktsii, ortogonalnoi po Sobolevu i porozhdennoi sistemoi Uolsha”, Mat. 20 Mezhdunar. Saratov. zimnei shkoly «Sovremennye problemy teorii funktsii i ikh prilozheniya» (Saratov, 28 yanvarya — 1 fevralya 2020 g.), Nauchnaya kniga, Saratov, 2020, 248–251

[5] Sharapudinov I. I., “Approksimativnye svoistva ryadov Fure po mnogochlenam, ortogonalnym po Sobolevu s vesom Yakobi i diskretnymi massami”, Mat. zametki., 101:4 (2017), 611–-629 | Zbl

[6] Sharapudinov I. I., “Spetsialnye ryady po polinomam Lagerra i ikh approksimativnye svoistva”, Sib. mat. zh., 58:2 (2017), 440–467 | MR | Zbl

[7] Sharapudinov I. I., “Sistemy funktsii, ortogonalnye po Sobolevu, assotsiirovannye s ortogonalnoi sistemoi”, Izv. RAN. Ser. mat., 82:1 (2018), 225–258 | MR | Zbl

[8] Sharapudinov I. I., “Ortogonalnye po Sobolevu sistemy funktsii i nekotorye ikh prilozheniya”, Usp. mat. nauk., 74:4 (448) (2019), 87–164 | MR | Zbl

[9] Sharapudinov I. I., Gadzhieva Z. D., “Polinomy, ortogonalnye po Sobolevu, porozhdennye mnogochlenami Meiksnera”, Izv. Saratov. un-ta. Nov. ser. Ser. Mat. Mekh. Inform., 16:3 (2016), 310–321 | MR | Zbl

[10] Sharapudinov I. I., Magomed-Kasumov M. G., Magomedov S. R., “Polinomy, ortogonalnye po Sobolevu, assotsiirovannye s polinomami Chebysheva pervogo roda”, Dagestan. elektron. mat. izv., 2015, no. 4, 1–14

[11] Sharapudinov I. I., Sharapudinov T. I., “Polinomy, ortogonalnye po Sobolevu, porozhdennye mnogochlenami Chebysheva, ortogonalnymi na setke”, Izv. vuzov. Mat., 2017, no. 8, 67–79 | Zbl

[12] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya. T. 2, Fizmatlit, M., 2001