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Russian Mathematical Surveys, 2019, Volume 74, Issue 4, Pages 659–733
DOI: https://doi.org/10.1070/RM9846 (Mi rm9846) 		 
This article is cited in 20 scientific papers (total in 20 papers)

Sobolev-orthogonal systems of functions and some of their applications

I. I. Sharapudinovab

a Daghestan Scientific Centre of Russian Academy of Sciences
b Vladikavkaz Scientific Centre of Russian Academy of Sciences
English version PDF (1055 kB) Citations (20)
References:
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DOI: https://doi.org/10.1070/RM9846
Abstract: Systems of functions are considered which are associated with a given orthogonal system and are orthogonal with respect to an inner product of Sobolev type involving terms with masses concentrated at a point. Special attention is paid to such systems generated by classical orthogonal systems such as the cosine system, the Haar system, and the systems of Legendre, Jacobi, and Laguerre polynomials. The approximation properties of Fourier series in Sobolev-orthogonal systems are investigated in several cases. For (generally speaking, non-linear) systems of differential equations deep connections between Sobolev-orthogonal systems and the Cauchy problem are considered.
Bibliography: 54 titles.
Keywords: Sobolev-orthogonal systems; Cauchy problem for a system of ordinary differential equations; systems generated by the Haar polynomials, the cosines, the Legendre, Jacobi, Laguerre polynomials.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00486-а
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00486-a).
Received: 30.07.2018
Russian version:
Uspekhi Matematicheskikh Nauk, 2019, Volume 74, Issue 4(448), Pages 87–164
DOI: https://doi.org/10.4213/rm9846
Bibliographic databases:
Document Type: Article
UDC: 517.538
MSC: 42C0533C45, 41A25
Language: English
Original paper language: Russian
Citation: I. I. Sharapudinov, “Sobolev-orthogonal systems of functions and some of their applications”, Uspekhi Mat. Nauk, 74:4(448) (2019), 87–164; Russian Math. Surveys, 74:4 (2019), 659–733
Citation in format AMSBIB
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    • This publication is cited in the following 20 articles:
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    References:57
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