On the boundary behavior of singular inner functions (Q1345494)

It is known that the radial boundary behavior of Blaschke products can be prescribed on any countable subset \(E\) of the unit circle \(T\). The author shows the following: Given any countable subset \(E = \{e^{i \theta_j} : j = 1,2, \cdots\}\) of \(T\) and any sequence \((a_j)\) of complex numbers with \(|a_j |\leq 1\), there exists a discrete singular inner function \(S\) having prescribed radial limits \(S^* (e^{i \theta}) = a_j\) \((j = 1,2, \ldots)\). She also adopts his method to the more general problem of prescribing radial cluster sets instead of radial limits in countably many points of \(T\).