Sobolev-orthogonal systems of functions associated with an orthogonal system

DOI10.1070/IM8536zbMath1395.42070OpenAlexW2791874372MaRDI QIDQ4568547

I. I. Sharapudinov

Publication date: 22 June 2018

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im8536

zbMATH Keywords

approximation properties of partial sums of Fourier series of Sobolev-orthogonal functionsconvergence of Fourier series of Sobolev-orthogonal functionsconvergence of Fourier series of Sobolev-orthogonal polynomials associated with Chebyshev polynomialsSobolev-orthogonal systems of functions associated with Chebyshev polynomialsSobolev-orthogonal systems of functions associated with Haar functions

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Other special orthogonal polynomials and functions (33C47) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)

Related Items (14)

On the representation of Sobolev systems orthogonal with respect to the inner product with one discrete point ⋮ Sobolev orthogonal polynomials associated with Chebyshev polynomials of the first kind and the Cauchy problem for ordinary differential equations ⋮ Hermite functions and inner product in Sobolev space ⋮ The uniform convergence of Fourier series in a system of polynomials orthogonal in the sense of Sobolev and associated to Jacobi polynomials ⋮ On the Uniform Convergence of the Fourier Series by the System of Polynomials Generated by the System of Laguerre Polynomials ⋮ RECURRENCE RELATIONS FOR SOBOLEV ORTHOGONAL POLYNOMIALS ⋮ Sobolev-orthogonal systems of functions and the Cauchy problem for ODEs ⋮ Sobolev-Orthonormal System of Functions Generated by the System of Laguerre Functions ⋮ Generalized trace formula for polynomials orthogonal in continuous-discrete Sobolev spaces ⋮ Sobolev-orthogonal systems of functions and some of their applications ⋮ A Sobolev orthogonal system of functions generated by a Walsh system ⋮ Sobolev orthogonal systems with two discrete points and Fourier series ⋮ Inner product and Gegenbauer polynomials in Sobolev space ⋮ Fractal Sobolev systems of functions associated with orthonormal systems of functions

Uses Software

• Matlab

Cites Work

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• On Sobolev orthogonal polynomials
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• Application of Chebyshev series for the integration of ordinary differential equations
• Sobolev orthogonal polynomials and second-order differential equations
• Orthogonal polynomials on Sobolev spaces: Old and new directions
• Laguerre polynomials generalized to a certain discrete Sobolev inner product space
• Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product
• Approximation properties of the Vallée-Poussin means of partial sums of a mixed series of Legendre polynomials
• Spectral Methods in MATLAB
• Approximation of functions of variable smoothness by Fourier-Legendre sums
• Approximation properties of mixed series in terms of Legendre polynomials on the classes $ {W^r}$
• Mean Convergence of Jacobi Series

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