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
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.
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.
|Russian Foundation for Basic Research
|This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00486-a).
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Russian Mathematical Surveys, 2019, 74:4, 659–733
MSC: 42C0533C45, 41A25
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
\paper Sobolev-orthogonal systems of functions and some of their applications
\jour Uspekhi Mat. Nauk
\jour Russian Math. Surveys
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