Zeros sets and radial zero sets in function spaces (Q1899785)

Functions \(f\) analytic in the unit disc are considered. There exists earlier results with integral conditions, where the set of zeros can be characterized in terms of moduli alone and other cases, where the angular distribution comes in. The latter is here shown to occur for a large class of functions with pointwise estimates of \(|f(z)|\). The method is to show that all zeros cannot be located on one radius, a case with integral containing a weight function is also taken up.