Real Analysis Exchange

Fourier Coefficients and Generalized Lipschitz Classes

S. S. Volosivets

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Abstract

In this paper we give some equivalence relations between behavior of Fourier coefficients of a special kind and smoothness of functions. A necessary and sufficient condition for existence of Schwartz derivative is also obtained.

Article information

Source
Real Anal. Exchange, Volume 34, Number 1 (2008), 219-226.

Dates
First available in Project Euclid: 19 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.rae/1242738933

Mathematical Reviews number (MathSciNet)
MR2527135

Zentralblatt MATH identifier
1180.42003

Subjects
Primary: 42A10: Trigonometric approximation
Secondary: 41A25: Rate of convergence, degree of approximation

Keywords
absolute convergence moduli of smoothness generalized Lipschitz classes

Citation

Volosivets, S. S. Fourier Coefficients and Generalized Lipschitz Classes. Real Anal. Exchange 34 (2008), no. 1, 219--226. https://projecteuclid.org/euclid.rae/1242738933


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References

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