Test functions in constrained interpolation

Abstract

We give a set of test functions for H 1 ∞ H_{1}^{\infty } , the algebra of bounded holomorphic functions on the disk with first derivative equal to 0 0 , whose interpolation problem was studied by Davidson, Paulsen, Raghupathi and Singh (2009). We show that this set of test functions is minimal by relating these ideas to realization and interpolation problems.