Sobolev-orthogonal systems of functions and some of their applications

被引：15

作者：

Sharapudinov, I. I. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Dagestan Sci Ctr, Makhachkala, Russia

[2] Russian Acad Sci, Vladikavkaz Sci Ctr, Vladikavkaz, Russia

来源：

RUSSIAN MATHEMATICAL SURVEYS | 2019年 / 74卷 / 04期

基金：

俄罗斯基础研究基金会;

关键词：

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; MIXED SERIES; APPROXIMATION PROPERTIES; CHEBYSHEV POLYNOMIALS; ULTRASPHERICAL POLYNOMIALS; LAGUERRE-POLYNOMIALS; FOURIER-SERIES; RESPECT; JACOBI; ASYMPTOTICS; OPERATORS;

D O I：

10.1070/RM9846

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：659 / 733

页数：75

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