Singular inner functions of L1-type II

Abstract

In the first paper of the same title, we introduced the concept of singular inner functions of $L^1$-type and obtained results for singular inner functions which are reminiscent of the results for weak infinite powers of Blaschke products. In this Paper, we investigate singular inner functions for discrete measures. We give equivalent conditions on a measure for which it is a Blaschke type. And we prove that two discrete measures are mutually singular if and only if the associated common zero sets of singular inner functions of $t_{+}^{\infty }$-type do not meet.