Basic Fourier series: convergence on and outside the q-linear grid

2006/05/30 by Cardoso, J. L.
#33D15 #42C10 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.math/0605764

Abstract

A q-type Holder 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 others conditions, one guaranties the (uniform) convergence of S_q[f] to f on and "outside" the set points of the q-linear grid.

Related

• Uniform convergence of Fourier-Bessel series on a q-linear grid
• Basic analog of Fourier series on a \large \que-quadratic grid
• A Simple Proof of the Uniform Convergence of Fourier Series Using Nonstandard Analysis
• Almost everywhere convergence of Fourier series on SU(2): the case of Holder continuous functions
• A primer on Fourier Series