Mathematical Sciences
Heinz
Langer
en
http://link.springer.com/10.1007/3-7643-7547-7_1
2006-01-01
true
2019-04-15T16:14
chapter
1-29
https://scigraph.springernature.com/explorer/license/
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.
Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-unitary Matrix Functions
chapters
2006
Springer Nature - SN SciGraph project
Daniel
Alpay
Ben-Gurion University of the Negev
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel
Dijksma
Aad
Alpay
Daniel
Interpolation, Schur Functions and Moment Problems
3-7643-7546-9
dimensions_id
pub.1002676549
Gohberg
Israel
Pure Mathematics
Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410, Mbarara, Uganda
Mbarara University of Science and Technology
0cbe7d85cb730b93086dd465370e2468c1319cef03ef27f2f62edc6cab92fb88
readcube_id
Birkhäuser-Verlag
Basel
Wanjala
Gerald
Department of Mathematics, University of Groningen, P.O. Box 800, NL-9700 AV Groningen, The Netherlands
University of Groningen
TU Wien
Institute of Analysis and Computational Mathematics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria
10.1007/3-7643-7547-7_1
doi