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All solutions to an operator Nevanlinna-Pick interpolation problem
(Springer, 2018)
The main results presented in this paper provide a complete and explicit description of all solutions to the left tangential operator Nevanlinna– Pick interpolation problem assuming the associated Pick operator is strictly ...
State space formulas for a suboptimal rational Leech problem I: maximum entropy solution
(Springer Verlag, 2014)
For the strictly positive case (the suboptimal case) the maximum entropy solution X to the Leech problem G(z)X(z) = K(z) and \({\|X\|_\infty={\rm sup}_{|z| \leq 1}\| X(z )\| \leq 1}\), with G and K stable rational matrix ...
State space formulae for stable rational matrix solutions of a Leech problem
(Elsevier, 2014)
Given stable rational matrix functions G and K, a procedure is presented to compute a stable rational
matrix solution X to the Leech problem associated with G and K, that is, G(z)X(z) = K(z) and sup|z|≤1
∥X(z)∥ ≤ 1. The ...
The Bézout equation on the right half-plane in a Wiener space setting
(Springer, 2017)
This paper deals with the Bézout equation G(s)X(s)=Im,Rs≤0, in the Wiener space of analytic matrix-valued functions on the right halfplane. In particular, G is an m × p matrix-valued analytic Wiener function, where p ≥ m, ...
The discrete twofold Ellis–Gohberg inverse problem
(Elsevier, 2017)
In this paper a twofold inverse problem for orthogonal matrix functions in the Wiener class is considered. The scalar-valued version of this problem was solved by Ellis and Gohberg in 1992. Under reasonable conditions, the ...
The twofold Ellis-Gohberg inverse problem in an abstract setting and applications
(Springer, 2019)
In this paper we consider a twofold Ellis–Gohberg type inverse problem in an abstract *-algebraic setting. Under natural assumptions, necessary and sufficient conditions for the existence of a solution are obtained, and ...
The twofold Ellis-Gohberg inverse problem for rational matrix functions on the real line
(Springer, 2020)
From the mid-1980s R.L. Ellis, I. Gohberg and D.C. Lay wrote several papers on systems of orthogonal matrix polynomials and matrix functions, culminating in the monograph [3] by Ellis and Gohberg, where additional background ...
Wiener-Hopf indices of unitary functions on the unit circle in terms of realizations and related results on Toeplitz operators
(Elsevier, 2017)
We provide new formulas for the Wiener–Hopf factorization indices of a rational matrix function which has neither poles nor zeros on the unit circle. In addition, we recover recent results on the Fredholm characteristics ...
The Bezout-Corona problem revisited: Wiener space setting
(Springer, 2016)
The matrix-valued Bezout-corona problem G(z)X(z)=Im, |z|<1, is studied in a Wiener space setting, that is, the given function G is an analytic matrix function on the unit disc whose Taylor coefficients are absolutely ...