caa a22 4500 477076963 CHVBK 20180405111440.0 cr unu---uuuuu 170330e19961201xx s 000 0 eng 10.1007/BF00047026 doi (NATIONALLICENCE)springer-10.1007/BF00047026 Zero-pole interpolation for meromophic matrix functions on an algebraic curve and transfer functions of 2D systems [Elektronische Daten] [Joseph Ball, Victor Vinnikov] We formulate and solve the problem of constructing a meromorphic bundle map over a compact Riemann surface X having a prescribed zero-pole structure (including directional information). The output bundle together with the zero-pole data is prespecified while the input bundle and the bundle map are to be determined. The Riemann surface X is assumed to be (birationally) embedded as an irreducible algebraic curve in ℙ2 and both input and output bundles are assumed to be equal to the kernels of determinantal representations for X. In this setting the solution can be found as the joint transfer function of a Livsic-Kravitsky two-operator commutative vessel (2D input-output dynamical system). Also developed is the basic theory of two-operator commutative vessels and the correct analogue of the transfer function for such a system (a meromorphic bundle map between input and output bundles defined over an algebraic curve associated with the vessel) together with a state space realization, a Mittag-Leffler type interpolation theorem and the state space similarity theorem for such bundle mappings. A more abstract version of the zero-pole interpolation problem is also presented. Kluwer Academic Publishers, 1996 zero-pole interpolation nationallicence meromorphic bundle map nationallicence vector bundles on a compact Riemann surface nationallicence determinantal representations of an algebraic curve nationallicence commutative 2D system (commutative vessel) nationallicence joint transfer function nationallicence Ball Joseph Department of Mathematics, Virginia Tech., 24061, Blacksburg, VA, U.S.A. aut Vinnikov Victor Department of Theoretical Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel aut Acta Applicandae Mathematica Kluwer Academic Publishers 45/3(1996-12-01), 239-316 0167-8019 45:3<239 1996 45 10440 https://doi.org/10.1007/BF00047026 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00047026 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ball Joseph Department of Mathematics, Virginia Tech., 24061, Blacksburg, VA, U.S.A aut NATIONALLICENCE 700 1- Vinnikov Victor Department of Theoretical Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 45/3(1996-12-01), 239-316 0167-8019 45:3<239 1996 45 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer