Equivalence of a $K$-functional with the approximation behavior of some linear means for abstract Fourier series
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- by Walter Trebels PDF
- Proc. Amer. Math. Soc. 127 (1999), 2883-2887 Request permission
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.References
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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
- Received by editor(s): December 3, 1997
- Published electronically: April 23, 1999
- Communicated by: Frederick W. Gehring
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2883-2887
- MSC (1991): Primary 41A65, 41A40, 33C45
- DOI: https://doi.org/10.1090/S0002-9939-99-05265-X
- MathSciNet review: 1654072