Journal of Fourier Analysis and Applications

, Volume 17, Issue 1, pp 96–114 | Cite as

Basic Fourier Series: Convergence on and Outside the q-Linear Grid

Article

Abstract

A q-type Hölder condition on a function f is given in order to establish (uniform) convergence of the corresponding basic Fourier series S q [f] to the function itself, on the set of points of the q-linear grid. Furthermore, by adding other conditions, one guarantees the (uniform) convergence of S q [f] to f on and “outside” the set points of the q-linear grid.

Keywords

q-trigonometric functions q-Fourier series Basic Fourier expansions Uniform convergence q-linear grid 

Mathematics Subject Classification (2000)

42C10 33D15 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.UTAD, Quinta de Prados, Edifício das Ciências Florestais, Departamento de MatemáticaCM-UTADVila RealPortugal

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