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Notation and preliminaries
Matrixvalued Schur and Caratheodory functions
An approach to the matricial Schur problem based
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apec Assume belongs Borel measure Cayley transform choice complex numbers Corollary corresponding Cpxq Cqxq defined diaq Dubovoj elementary factor F(dz factor with pole full-rank normalized given H. A. Schwarz Hence Hermitian matrix holds true holomorphic implies interpolation problems J-contractive J-Hermitian J-negative definite J-positive definite Let F Let n e linear fractional transformations matrix balls matrix polynomials matrix-valued function Moreover nank non-degenerate Schur sequence non-singular non-singular matrix normalized J elementary nq n nq nq np obtain orthonormal systems pole of order positive Hermitian Potapov Proposition 4.2.1 pxp unitary pxq non-degenerate Schur pxq Schur function pxq Schur sequence qxq matrix readily checked Remark resolvent matrix satisfied Schur parameters Schur problem signature matrix statements are equivalent subspace of Cq Suppose Szego pair Taylor coefficients Taylor series representation Theorem unitary matrix yields