Description of Helson-Szegö measures in terms of the Schur parameter sequences of associated Schur functions

Abstract

Let mu be a probability measure on the Borelian sigma-algebra of the unit circle. Then we associate a Schur function theta in the unit disk with mu and give characterizations of the case that mu is a Helson-Szegö measure in terms of the sequence of Schur parameters of theta.

29 pages; Typos corrected in Section 6; Section 6 revised and extended; Typo corrected on page 27;