Titlebook: Current Trends in Operator Theory and its Applications; Joseph A. Ball,J. William Helton,Leiba Rodman Conference proceedings 2004 Springer

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Strongly Regular ,-Inner Matrix Functions and Related Problems,Hilbert spaces and formulas for the reproducing kernels of these spaces are reviewed. Applications to bitangential interpolation problems, bi-tangential inverse problems for canonical integral and differential systems, J-unitary nodes and Livsic-Brodskii J-nodes are surveyed. Most of the furnished i

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Admissibility of Control and Observation Operators for Semigroups: A Survey,h to infinite-dimensional systems theory. The themes discussed include duality between control and observation, conditions for admissibility expressed in terms of the resolvent of the infinitesimal generator, results for normal semigroups and their links with Carleson measures, properties of shift s

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,On the Bessmertny? Class of Homogeneous Positive Holomorphic Functions of Several Variables,eal parts there and take selfadjoint operator values at real points, and its subclass consisting of functions representable in the form of Schur complement of a block of a linear pencil of operators with positive semidefinite operator coefficients, are investigated. The latter subclass is a generali

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Rational Solutions of the Schlesinger System and Isoprincipal Deformations of Rational Matrix Functequations and holomorphic deformations. We introduce the terminology “isoprincipal” for the deformations of Fuchsian equations with general (not necessarily non-resonant) matrix coefficients corresponding to solutions of the Schlesinger system. Every isoprincipal deformation is isomonodromic. The co