Pointwise universal trigonometric series

A series is called a pointwise universal trigonometric series if for any f∈C(T), there exists a strictly increasing sequence {nk}k∈N of positive integers such that converges to f(z) pointwise on T. We find growth conditions on coefficients allowing and forbidding the existence of a pointwise universal trigonometric series. For instance, if as |n|→∞ for some ε>0, then the series Sa cannot be pointwise universal. On the other hand, there exists a pointwise universal trigonometric series Sa with as |n|→∞.