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, p⩾1, r=1,2,… is proved.
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
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\by M.~G.~Magomed-Kasumov
\paper A Sobolev Orthogonal System of Functions Generated by a Walsh System
\jour Mat. Zametki
\yr 2019
\vol 105
\issue 4
\pages 545--552
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\jour Math. Notes
\yr 2019
\vol 105
\issue 4
\pages 543--549
\crossref{https://doi.org/10.1134/S0001434619030271}
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Linking options:
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https://doi.org/10.4213/mzm12069
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This publication is cited in the following 7 articles:
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
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
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
M. G. Magomed-Kasumov, “Sobolev orthogonal systems with two discrete points and Fourier series”, Russian Math. (Iz. VUZ), 65:12 (2021), 47–55
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
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
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