Abstract
Let 𝜇 be a probability measure on the Borelian 𝜎-algebra of the unit circle. Then we associate a Schur function 𝜃 in the unit disk with 𝜇 and give characterizations of the case that 𝜇 is a Helson-Szeg?o measure in terms of the sequence of Schur parameters of 𝜃. Furthermore, we state some connections of these characterizations with the backward shift.
Mathematics Subject Classification (2000). Primary 30E05, 47A57.
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Dubovoy, V.K., Fritzsche, B., Kirstein, B. (2012). Description of Helson-Szegő Measures in Terms of the Schur Parameter Sequences of Associated Schur Functions. In: Dym, H., Kaashoek, M., Lancaster, P., Langer, H., Lerer, L. (eds) A Panorama of Modern Operator Theory and Related Topics. Operator Theory: Advances and Applications(), vol 218. Springer, Basel. https://doi.org/10.1007/978-3-0348-0221-5_11
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