Zero sets of interpolating Blaschke products (Q1067175)

Let \(H^{\infty}\) be the space of boundary functions of bounded analytic functions on the open unit disk. For a function h in \(H^{\infty}\), Z(h) denotes the zero set of h in the maximal ideal space of \(H^{\infty}+C\). It is well known that if b is an interpolating Blaschke product then Z(b) is an interpolation set for \(H^{\infty}\). It is proved that the converse of the above fact is almost true. The main theorem is: If a function h is in \(H^{\infty}\) and Z(h) is an interpolation set for \(H^{\infty}\), then there is an interpolating Blaschke product b such that \(Z(b)=Z(h)\). Also some of its applications are given.