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Small gaps Fourier series and generalized variations
-
Rajendra G. Vyas
Published/Copyright:
March 27, 2012
Abstract.
Suppose 
has a Fourier series 
(
) with small gaps 
for all 
. Here, by applying the Wiener–Ingham result for finite trigonometric sum with `small' gaps, we estimate the order of magnitude of the Fourier coefficients and obtain a sufficient condition for the convergence of the series 
(
) if 
is locally of class 
.
Keywords.: Fourier series with small gaps; Fourier coefficients; ; -absolute convergence of Fourier series
Received: 2011-08-19
Revised: 2012-02-02
Accepted: 2012-02-02
Published Online: 2012-03-27
Published in Print: 2012-April
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Fourier series with small gaps;
Fourier coefficients;
-absolute convergence of Fourier series
Articles in the same Issue
- Masthead
- Spectrum of the finite Dunkl transform operator and Donoho–Stark uncertainty principle
- A priori estimates of Nodal solutions on the annulus for some PDE and their Morse index
- Combined Sundman–Darboux transformations and solutions of nonlinear ordinary differential equations of second order
- Multiresolution analysis on local fields and characterization of scaling functions
- Multiplicity of positive solution of -Laplacian problems with sign-changing weight functions
- Small gaps Fourier series and generalized variations
- Central limit theorems for radial random walks on matrices for
