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.
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Communicated by Hans G. Feichtinger.
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Cardoso, J.L. Basic Fourier Series: Convergence on and Outside the q-Linear Grid. J Fourier Anal Appl 17, 96–114 (2011). https://doi.org/10.1007/s00041-010-9161-2
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DOI: https://doi.org/10.1007/s00041-010-9161-2