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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Equivalence of a $K$-functional with the approximation behavior of some linear means
for abstract Fourier series


Author: Walter Trebels
Journal: Proc. Amer. Math. Soc. 127 (1999), 2883-2887
MSC (1991): Primary 41A65, 41A40, 33C45
Published electronically: April 23, 1999
MathSciNet review: 1654072
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Abstract: Within the setting of abstract Cesàro-bounded Fourier series a $K$-functional is introduced and characterized by the convergence behavior of some linear means. Applications are given within the framework of Jacobi, Laguerre and Hermite expansions. In particular, Ditzian's (1996) equivalence result in the setting of Legendre expansions is covered.


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Additional Information

Walter Trebels
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstr. 7, D–64289 Darmstadt, Germany
Email: trebels@mathematik.tu-darmstadt.de

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05265-X
PII: S 0002-9939(99)05265-X
Keywords: $K$-functional, linear approximation processes, saturation, orthogonal expansions
Received by editor(s): December 3, 1997
Published electronically: April 23, 1999
Communicated by: Frederick W. Gehring
Article copyright: © Copyright 1999 American Mathematical Society