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