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

Chapter
Part of the Operator Theory: Advances and Applications book series (OT, 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).

Keywords

Shift coshift contraction unitary colligation characteristic operator function Schur function Schur parameters pseudocontinuability of Schur functions 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  1. 1.Department of Mathematics and MechanicsState UniversityKharkovUkraine

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