books.google.com - Let $f$ be a periodic measurable function and $(n_k)$ an increasing sequence of positive integers. The authors study conditions under which the series $\sum_{k=1}^\infty c_k f(n_kx)$ converges in mean and for almost every $x$. There is a wide classical literature on this problem going back to the 30's,...http://books.google.com/books/about/On_the_Convergence_of_summation_Symbol_c.html?id=mtzo5u7Ir2AC&utm_source=gb-gplus-shareOn the Convergence of [summation Symbol]c[subscript K]f(n[subscript K]x)