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Shift Operators Contained in Contractions, Schur Parameters and Pseudocontinuable Schur Functions

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Interpolation, Schur Functions and Moment Problems

Part of the book series: Operator Theory: Advances and Applications ((LOLS,volume 165))

Abstract

The main goal of the paper is to study the properties of the Schur parameters of the noninner functions of the Schur class S which admit a pseudocontinuation. To realize this aim we construct a model of completely nonunitary contraction in terms of Schur parameters of its characteristic function (see Chapters 2 and 3). By means of the constructed model a quantitative criterion of pseudocontinuability is established (see Chapter 4 and Sections 5.1 and 5.2). The properties of the Schur parameter sequences of pseudocontinuable noninner Schur functions are studied (see Sections 5.3 and 5.4).

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Author information

Authors and Affiliations

  1. Department of Mathematics and Mechanics, State University, Svobody Square 4, 61077, Kharkov, Ukraine

    V. K. Dubovoy

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  1. V. K. Dubovoy
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Editors and Affiliations

  1. Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva, 84105, Israel

    Daniel Alpay

  2. School of Mathematical Sciences, Raymond and Beverly Sackler, Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Israel Gohberg

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Dubovoy, V.K. (2006). Shift Operators Contained in Contractions, Schur Parameters and Pseudocontinuable Schur Functions. In: Alpay, D., Gohberg, I. (eds) Interpolation, Schur Functions and Moment Problems. Operator Theory: Advances and Applications, vol 165. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7547-7_5

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