A Generic Schur Function is an Inner One

Abstract

A Schur function sis a function which is holomorphic in an open unit disk \(\mathbb{D}\) of the complex plane and is contractive there for |s(z)|≤1 for \(z \in \mathbb{D}\). A Schur function is called exceptional if it is rational inner one. A contractive sequence w is a sequence w={γk}0≤ - \infty } \), then for p μ almost every Schur function the sequence of its Schur approximants converges pointwise almost everywhere (with respect to the Lebesgue measure) on the unit circle. The multiplicative ergodic theory is the main tool of investigation.