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


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2006

AUTHORS

Daniel Alpay , Aad Dijksma , Heinz Langer , Gerald Wanjala

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 z 1 ∈ \( \mathbb{T}\). 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 z 1 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. More... »

PAGES

1-29

Book

TITLE

Interpolation, Schur Functions and Moment Problems

ISBN

3-7643-7546-9

From Grant

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/3-7643-7547-7_1

DOI

http://dx.doi.org/10.1007/3-7643-7547-7_1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1002676549


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