Zero-pole interpolation for meromorphic matrix functions on an algebraic curve and transfer functions of 2D systems

DOI10.1007/BF00047026zbMath0861.47010MaRDI QIDQ2563462

Victor Vinnikov, Joseph A. Ball

Publication date: 11 May 1997

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

zbMATH Keywords

compact Riemann surfacejoint transfer functiondeterminantal representations of an algebraic curveinput bundleLivsic-Kravitsky two-operator commutative vesselmeromorphic bundle mapMittag-Leffler type interpolation theoremstate space similarity theoremzero-pole interpolation problemzero-pole structure

Mathematics Subject Classification ID

Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Special algebraic curves and curves of low genus (14H45) Linear operator methods in interpolation, moment and extension problems (47A57) Vector bundles on curves and their moduli (14H60) Canonical models for contractions and nonselfadjoint linear operators (47A45) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48)

Related Items (16)

Representations of Lie algebras by non-skewselfadjoint operators in Hilbert space ⋮ Canonical Transfer-function Realization for Schur-Agler-class Functions of the Polydisk ⋮ Noncommutative convexity arises from linear matrix inequalities ⋮ Ahlfors problem for polynomials ⋮ A behavioral interpretation of Livšic systems ⋮ de Branges spaces on compact Riemann surfaces and a Beurling-Lax type theorem ⋮ Interpolation in multivariable de Branges-Rovnyak spaces ⋮ Construction of Hardy spaces on Riemann surfaces with boundaries ⋮ Commuting operators over Pontryagin spaces with applications to system theory ⋮ Determinantal representations of singular hypersurfaces in \(\mathbb P^n\) ⋮ Interpolation problems for holomorphic functions ⋮ Pole placement for overdetermined 2D systems ⋮ Indefinite Hardy spaces on finite bordered Riemann surfaces ⋮ Livsic-type determinantal representations and hyperbolicity ⋮ Stable and real-zero polynomials in two variables ⋮ LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future

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