Pointwise convergence of almost periodic Fourier series and associated series of dilates

Christophe Cuny, Michel Weber

Let ${\mathcal{S}}^2$ be the Stepanov space and let ${\lambda }_n\uparrow \infty$. Let $(a_n{)}_{n\ge 1}$ be satisfying Wiener's condition $A:= \sum_{n\ge 1} \big(\sum_{k\, :\, n\le λ_k \le n+1}…