Journal of Fourier Analysis and Applications

, Volume 17, Issue 1, pp 96–114

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


DOI: 10.1007/s00041-010-9161-2

Cite this article as:
Cardoso, J.L. J Fourier Anal Appl (2011) 17: 96. doi:10.1007/s00041-010-9161-2


A q-type Hölder condition on a function f is given in order to establish (uniform) convergence of the corresponding basic Fourier series Sq[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 Sq[f] to f on and “outside” the set points of the q-linear grid.


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

Mathematics Subject Classification (2000)

42C10 33D15 

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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