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Uspekhi Mat. Nauk, 2019, Volume 74, Issue 4(448), Pages 87–164 (Mi umn9846)  

This article is cited in 2 scientific papers (total in 2 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

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).


DOI: https://doi.org/10.4213/rm9846

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English version:
Russian Mathematical Surveys, 2019, 74:4, 659–733

Bibliographic databases:

UDC: 517.538
MSC: 42C0533C45, 41A25
Received: 30.07.2018

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Manas-Manas J.F., Moreno-Balcazar J.J., Wellman R., “Eigenvalue Problem For Discrete Jacobi-Sobolev Orthogonal Polynomials”, Mathematics, 8:2 (2020), 182  crossref  isi
    2. M. S. Sultanakhmedov, “Recurrence relations for Sobolev orthogonal polynomials”, Probl. anal. Issues Anal., 9(27):2 (2020), 97–118  mathnet  crossref
  • Успехи математических наук Russian Mathematical Surveys
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