Weithed Spaces of Pseudocontinuable Functions and Approximations by Rational Functions with Prescribed Poles

Abstract

The main result of this paper provides an essential intermediate step for the proof of the authors theorem on left and right Blaschke-Potapov products which yields more insight into the structure of $J$-inner functions. The goal of this paper is to prepare an appropriate backward Schur-Potapov algorithm by solving a weighted approximation problem.