Sobolev-orthogonal systems of functions and some of their applications
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...
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| Veröffentlicht in: | Russian mathematical surveys 2019-08, Vol.74 (4), p.659-733 |
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| container_title | Russian mathematical surveys |
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| creator | Sharapudinov, I. I. |
| description | 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. |
| doi_str_mv | 10.1070/RM9846 |
| format | Article |
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I.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c315t-d4e8ba74814d0be82d1c055d093ea23d756571127e8ed5de9dff45c7ebeafa983</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Cauchy problems</topic><topic>Differential equations</topic><topic>Fourier series</topic><topic>Jacobi</topic><topic>Laguerre polynomials</topic><topic>Mathematical analysis</topic><topic>Nonlinear equations</topic><topic>Nonlinear systems</topic><topic>Polynomials</topic><topic>Sobolev-orthogonal systems; Cauchy problem for a system of ordinary differential equations; systems generated by the Haar polynomials</topic><topic>the cosines</topic><topic>the Legendre</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sharapudinov, I. 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| ispartof | Russian mathematical surveys, 2019-08, Vol.74 (4), p.659-733 |
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| language | eng |
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| source | HEAL-Link subscriptions: Institute of Physics (IOP) Journals; Institute of Physics Journals; Alma/SFX Local Collection |
| subjects | Cauchy problems Differential equations Fourier series Jacobi Laguerre polynomials Mathematical analysis Nonlinear equations Nonlinear systems Polynomials Sobolev-orthogonal systems Cauchy problem for a system of ordinary differential equations systems generated by the Haar polynomials the cosines the Legendre |
| title | Sobolev-orthogonal systems of functions and some of their applications |
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