On extended eigenvalues and extended eigenvectors of truncated shift

In this paper we consider the truncated shift operator S-u on the model space K-u(2) := H-2 circle minus u H-2. We say that a complex number lambda is an extended eigenvalue of S-u if there exists a nonzero operator X, called extended eigenvector associated to lambda, and satisfying the equation S-u X = lambda XSu. We give a complete description of the set of extended eigenvectors of S-u, in the case of u is a Blaschke product.