Mean convergence of generalized Jacobi series and interpolating polynomials. I

DOI10.1006/jath.1993.1019zbMath0781.42026OpenAlexW1990422808MaRDI QIDQ1801545

Yuan Xu

Publication date: 10 February 1994

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.1993.1019

zbMATH Keywords

weighted norm inequalitiesgeneralized Jacobi weight functionsweighted mean convergencegeneralized Jacobi seriesweighted norm convergence

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Approximation by polynomials (41A10)

Related Items (12)

Necessary and sufficient conditions for mean convergence of orthogonal expansions for Freud weights ⋮ Mean convergence of Hermite interpolation revisited ⋮ Pointwise bounds of orthogonal expansions on the real line via weighted Hilbert transforms ⋮ Marcinkiewicz-Zygmund inequalities and the numerical approximation of singular integrals for exponential weights: Methods, results and open problems, some new, some old ⋮ Stieltjes polynomials and Lagrange interpolation ⋮ Fourier series of Gegenbauer-Sobolev polynomials ⋮ A survey on mean convergence of interpolatory processes ⋮ Universality limits for generalized Jacobi measures ⋮ Orthogonal polynomials and expansions for a family of weight functions in two variables ⋮ Dirichlet Theorem for Jacobi-Dunkl Expansions ⋮ Bounded quasi-interpolatory polynomial operators ⋮ Legendre polynomials of the second kind, Fourier series and Lagrange interpolation

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