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The Pelczynski and Dunford-Pettis properties of the space of uniform convergent fourier series with respect to orthogonal polynomials.

Colloq. Math. 164, 1-9 (2021)
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Open Access Green as soon as Postprint is submitted to ZB.
The Banach space U(mu) of uniformly convergent Fourier series with respect to an orthonormal polynomial sequence with orthogonalization measure mu supported on a compact set S subset of R is studied. For certain measures mu, involving Bernstein-Szego polynomials and certain Jacobi polynomials, it is proven that U(mu) has the Pelczyriski property, and also that U(mu) and U(mu)* have the Dunford-Pettis property.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Orthogonal Polynomials ; Fourier Series ; Uniform Convergence ; Pelczynski Property ; Dunford-pettis Property ; Bernstein-szego Polynomials ; Jacobi Polynomials
ISSN (print) / ISBN 0010-1354
e-ISSN 1730-6302
Quellenangaben Volume: 164, Issue: 1, Pages: 1-9 Article Number: , Supplement: ,
Publisher Institute of Mathematics, Polish Academy of Sciences
Publishing Place Krakowskie Przedmiescie 7 Po Box 1001, 00-068 Warsaw, Poland
Reviewing status Peer reviewed