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

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

2006-05-30

arxiv.org/abs/math/0605764v1

Mathematics

General Mathematics

16 pages

Scientific paper

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.

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