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Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-unitary Matrix Functions

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

Abstract

We define and solve a boundary interpolation problem for generalized Schur functions s(z) on the open unit disk \( \mathbb{D}\) which have preassigned asymptotics when z from \( \mathbb{D}\) tends nontangentially to a boundary point z1\( \mathbb{T}\). The solutions are characterized via a fractional linear parametrization formula. We also prove that a rational J-unitary 2 × 2-matrix function whose only pole is at z1 has a unique minimal factorization into elementary factors and we classify these factors. The parametrization formula is then used in an algorithm for obtaining this factorization. In the proofs we use reproducing kernel space methods.

Keywords

Generalized Schur function Boundary interpolation Rational J-unitary matrix function Minimal factorization Elementary factor Brune section Reproducing kernel space Indefinite metric 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.Department of MathematicsUniversity of GroningenGroningenThe Netherlands
  3. 3.Institute of Analysis and Computational MathematicsVienna University of TechnologyViennaAustria
  4. 4.Department of MathematicsMbarara University of Science and TechnologyMbararaUganda

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