Basic Fourier Series: Convergence on and Outside the q-Linear Grid
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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.
Keywordsq-trigonometric functions q-Fourier series Basic Fourier expansions Uniform convergence q-linear grid
Mathematics Subject Classification (2000)42C10 33D15
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