Schur Algorithm for the Integral Representations of Lacunary Hankel Forms

Abstract

A Schur type algorithm for the lacunary Nehari problem making use of the extensions of certain isometrics is shown. A parametrization of the solution set is also obtained. A constructive method that provides the solutions by a sequence of Schur type parameters is developed. In the case of the classical Nehari problem, this algorithm gives the classical Schur parameters for the Carathéodory-Fejér interpolation problem. Here we propose another way to solve this problem, namely as an application of the Nehaii problem via the problem of the extension of isometrics associated to it. This point of view will lead in a forthcoming paper to the generalization of the results to the matricial case.