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Matematicheskie Zametki, 2019, Volume 105, Issue 4, Pages 545–552
DOI: https://doi.org/10.4213/mzm12069
(Mi mzm12069)
 

This article is cited in 7 scientific papers (total in 7 papers)

A Sobolev Orthogonal System of Functions Generated by a Walsh System

M. G. Magomed-Kasumovab

a Vladikavkaz Scientific Centre of the Russian Academy of Sciences
b Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
Full-text PDF (447 kB) Citations (7)
References:
Abstract: Properties of functions from the Sobolev orthogonal system Wr generated by the Walsh system are studied. In particular, recurrence relations for functions from W1 are obtained. The uniform convergence of Fourier series in the system Wr to functions f from the Sobolev spaces WrLp, p1, r=1,2, is proved.
Keywords: Sobolev orthogonality, Walsh system, uniform convergence, recurrence relation.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-00477
This work was supported by the Russian Foundation for Basic Research under grant 18-31-00477 mol_a.
Received: 23.05.2018
Revised: 10.07.2018
English version:
Mathematical Notes, 2019, Volume 105, Issue 4, Pages 543–549
DOI: https://doi.org/10.1134/S0001434619030271
Bibliographic databases:
Document Type: Article
UDC: 517.521
Language: Russian
Citation: M. G. Magomed-Kasumov, “A Sobolev Orthogonal System of Functions Generated by a Walsh System”, Mat. Zametki, 105:4 (2019), 545–552; Math. Notes, 105:4 (2019), 543–549
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm12069
  • https://doi.org/10.4213/mzm12069
  • https://www.mathnet.ru/eng/mzm/v105/i4/p545
  • This publication is cited in the following 7 articles:
    1. M. G. Magomed-Kasumov, “The Uniform Convergence of Fourier Series in a System of the Sobolev Orthogonal Polynomials Associated to Ultraspherical Jacobi Polynomials”, Sib Math J, 65:6 (2024), 1343  crossref
    2. M. G. Magomed-Kasumov, “Sobolevskie sistemy, ortogonalnye otnositelno vesovogo skalyarnogo proizvedeniya s dvumya diskretnymi tochkami, i ryady Fure po nim”, Izv. vuzov. Matem., 2024, no. 11, 35–50  mathnet  crossref
    3. M. G. Magomed-Kasumov, “The uniform convergence of Fourier series in a system of polynomials orthogonal in the sense of Sobolev and associated to Jacobi polynomials”, Siberian Math. J., 64:2 (2023), 338–346  mathnet  crossref  crossref  mathscinet
    4. M. G. Magomed-Kasumov, “Sobolev orthogonal systems with two discrete points and Fourier series”, Russian Math. (Iz. VUZ), 65:12 (2021), 47–55  mathnet  crossref  crossref
    5. M. G. Magomed-Kasumov, “Otsenki skorosti skhodimosti ryadov Fure po ortogonalnoi v smysle Soboleva sisteme funktsii, porozhdennoi sistemoi Uolsha”, Materialy 20 Mezhdunarodnoi Saratovskoi zimnei shkoly «Sovremennye problemy teorii funktsii i ikh prilozheniya», Saratov, 28 yanvarya — 1 fevralya 2020 g.  Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 200, VINITI RAN, M., 2021, 73–80  mathnet  crossref
    6. M. G. Magomed-Kasumov, S. R. Magomedov, “Bystroe preobrazovanie Fure po sisteme funktsii, ortogonalnykh po Sobolevu i porozhdennykh sistemoi Uolsha”, Dagestanskie elektronnye matematicheskie izvestiya, 2021, no. 15, 55–66  mathnet  crossref
    7. R. M. Gadzhimirzaev, “O ravnomernoi skhodimosti ryada Fure po sisteme polinomov, porozhdennoi sistemoi polinomov Lagerra”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 20:4 (2020), 416–423  mathnet  crossref
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