Equivalence of a -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 | References | Similar Articles | Additional Information

Abstract: Within the setting of abstract Cesàro-bounded Fourier series a -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:
https://doi.org/10.1090/S0002-9939-99-05265-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