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.
The research for this paper was supported in part by the Center for Advanced Studies in Mathematics, Ben-Gurion University of the Negev and by the Netherlands Organization of Scientific Research NWO (grant B61-524).
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Alpay, D., Dijksma, A., Langer, H., Wanjala, G. (2006). Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-unitary Matrix Functions. In: Alpay, D., Gohberg, I. (eds) Interpolation, Schur Functions and Moment Problems. Operator Theory: Advances and Applications, vol 165. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7547-7_1
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