Alpay, Daniel

Dijksma, Aad

Langer, Heinz

Wanjala, Gerald

English

We define and solve a boundary interpolation problem for generalized Schur functions s(z) on the open unit disk D which have preassigned asymptotics when z from D tends nontangentially to a boundary point z1 ∈ 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

Dissertations of the University of Groningen

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

https://pure.rug.nl/ws/files/10633448/2006OperThAdvApplAlpay.pdf

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

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Dissertations of the University of Groningen