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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Walter Trebels
Journal: Proc. Amer. Math. Soc. 127 (1999), 2883-2887.
MSC (1991): Primary 41A65, 41A40, 33C45
Posted: April 23, 1999
MathSciNet review: 1654072
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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.

References:

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2.: P.L. Butzer, R.J. Nessel, and W. Trebels, On summation processes of Fourier expansions in Banach spaces. I Comparison theorems; II Saturation theorems, Tohôku Math. J. 24 (1972), 127 - 140; 551 - 569.MR 48:9196; MR 48:9197
3.: Z. Ditzian, A $K$ -functional and the rate of convergence of some linear polynomial operators, Proc. Amer. Math. Soc. 124 (1996), 1773 - 1781. MR 96h:41026
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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: 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
Posted: April 23, 1999
Communicated by: Frederick W. Gehring
Copyright of article: Copyright 1999, American Mathematical Society

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