Displaying similar documents to “Dual Szegő pairs of sequences of rational matrix-valued functions.”

Reproducing kernels and Riccati equations

Harry Dym (2001)

International Journal of Applied Mathematics and Computer Science

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The purpose of this paper is to exhibit a connection between the Hermitian solutions of matrix Riccati equations and a class of finite dimensional reproducing kernel Krein spaces. This connection is then exploited to obtain minimal factorizations of rational matrix valued functions that are J-unitary on the imaginary axis in a natural way.

Explicit rational solutions of Knizhnik-Zamolodchikov equation

Lev Sakhnovich (2008)

Open Mathematics

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We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions generated by elements of the symmetric group 𝒮 n n. We assume that parameter ρ = ±1. In previous paper [5] we proved that the fundamental solution of the corresponding KZ-equation is rational. Now we construct this solution in the explicit form.

Inertias and ranks of some Hermitian matrix functions with applications

Xiang Zhang, Qing-Wen Wang, Xin Liu (2012)

Open Mathematics

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Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f(X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX =B and YC = D respectively....