Ontology type: schema:Chapter Open Access: True
2006
AUTHORSDaniel Alpay , Aad Dijksma , Heinz Langer , Gerald Wanjala
ABSTRACTWe 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... »
PAGES1-29
Interpolation, Schur Functions and Moment Problems
ISBN3-7643-7546-9
http://scigraph.springernature.com/pub.10.1007/3-7643-7547-7_1
DOIhttp://dx.doi.org/10.1007/3-7643-7547-7_1
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