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On the Absolute Convergence of Fourier Series
Published/Copyright:
March 3, 2010
Abstract
The necessary and sufficient conditions of the absolute convergence of a trigonometric Fourier series are established for continuous 2ฯ-periodic functions which in [0, 2ฯ] have a finite number of intervals of convexity, and whose ๐th Fourier coefficients are O(ฯ(1/๐; ๐)/๐), where ฯ(ฮด; ๐) is the continuity modulus of the function ๐.
Key words and phrases.: Periodic funcctions with a finite number of intervals of convexity; absolute convergence of Fourier series; estimates of Fourier coefficients
Received: 1995-06-02
Published Online: 2010-03-03
Published in Print: 1997-August
ยฉ 1997 Plenum Publishing Corporation
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Articles in the same Issue
- A Multidimensional Singular Boundary Value Problem of the CauchyโNicoletti Type
- Non-Abelian Cohomology of Groups
- On the Absolute Convergence of Fourier Series
- On the Solvability of the Multidimensional Version of the First Darboux Problem for a Model Second-Order Degenerating Hyperbolic Equation
- On the Global Solvability of the Cauchy Problem for Singular Functional Differential Equations
- Weighted Composition Operators on Bergman and Dirichlet Spaces
- Modular Properties of Theta-Functions and Representation of Numbers by Positive Quadratic Forms
