For a function h in H∞,
Z(h) denotes the zero set of h in the maximal ideal space of H∞+ C. It is
well known that if q is an interpolating Blaschke product then Z(q) is an
interpolation set for H∞. The purpose of this paper is to study the converse of
the above result. Our theorem is: If a function h is in H∞ and Z(h) is an
interpolation set for H∞, then there is an interpolating Blaschke product
q such that Z(q) = Z(h). As applications, we will study that for a given
interpolating Blaschke product q, which closed subsets of Z(q) are zero sets for some
functions in H∞. We will also give a characterization of a pair of interpolating
Blaschke products q1 and q2 such that Z(q1) ∪ Z(q2) is an interpolation set for
H∞.
