The Pełczyński and Dunford–Pettis properties of the space of uniform convergent Fourier series with respect to orthogonal polynomials

DOI10.4064/CM7890-3-2020zbMath1478.46010OpenAlexW3048282527MaRDI QIDQ4997523

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Publication date: 29 June 2021

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/cm7890-3-2020

zbMATH Keywords

orthogonal polynomialsuniform convergenceJacobi polynomialsDunford-Pettis propertyFourier seriesBernstein-Szegő polynomialsPełczyński property

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Isomorphic theory (including renorming) of Banach spaces (46B03) Banach spaces of continuous, differentiable or analytic functions (46E15)

Cites Work

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• Nonnegative linearization for little \(q\)-Laguerre polynomials and Faber basis
• The Pełczyński property for tight subspaces
• A continuous function space with a Faber basis.
• The Dunford-Pettis property for certain planar uniform algebras
• A Wiener theorem for orthogonal polynomials
• Orthogonal polynomials of discrete variable and boundedness of Dirichlet kernel
• The Dunford-Pettis property for the ball-algebras, the polydisc-algebras and the Sobolev spaces
• An Introduction to Banach Space Theory
• Sur Les Applications Lineaires Faiblement Compactes D'Espaces Du Type C(K)

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