Basic Fourier series: convergence on and outside the \(q\)-linear grid (Q628714)

In order to establish (uniform) convergence of the corresponding basic Fourier series \(S_q[f]\) to the function \(f\) itself, on the set of points of the \(q\)-linear grid, a \(q\)-type Hölder condition on the function \(f\) is obtained. The (uniform) convergence of \(S_q[f]\) to \(f\) on and outside the set of points of the \(q\)-linear grid is also guaranteed by adding other conditions.