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Titlebook: Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations; Daniel Alpay,Victor Vinnikov Book 2005 Birkh�user

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书目名称Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations
编辑Daniel Alpay,Victor Vinnikov
视频video
概述Focussed selection of invited contributions of experts in the area.Establishing ‘multidimensional operator theory‘ as a working field
丛书名称Operator Theory: Advances and Applications
图书封面Titlebook: Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations;  Daniel Alpay,Victor Vinnikov Book 2005 Birkh�user
描述.Operator theory, system theory, scattering theory, and the theory of analytic functions of one complex variable are deeply related topics, and the relationships between these theories are well understood. When one leaves the setting of one operator and considers several operators, the situation is much more involved. There is no longer a single underlying theory, but rather different theories, some of them loosely connected and some not connected at all. These various theories, which one could call "multidimensional operator theory", are topics of active and intensive research..The present volume contains a selection of papers in multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations..The volume will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoreticalphysicists..
出版日期Book 2005
关键词Funktionentheorie; Operator theory; Operatortheorie; Systemtheorie; calculus; differential equation; ortho
版次1
doihttps://doi.org/10.1007/b137040
isbn_ebook978-3-7643-7303-0Series ISSN 0255-0156 Series E-ISSN 2296-4878
issn_series 0255-0156
copyrightBirkh�user Basel 2005
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One-Sided Tangential Interpolation for Hilbert-Schmidt Operator Functions with Symmetries on the Bionsidered: (a) componentwise symmetries that operate separately on each component of a general point in the bidisk; (b) interchange symmetry that interchanges the two components of a general point in the bidisk. Applications are made to multipoint tangential interpolation problems of special form.
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Functional Models for Representations of the Cuntz Algebra,pace up to unitary equivalence. As an illustration, we compute the weighting matrix for the free atomic representations studied by Davidson and Pitts and the related permutative representations studied by Bratteli and Jorgensen.
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0255-0156 or theory, system theory, scattering theory, and the theory of analytic functions of one complex variable are deeply related topics, and the relationships between these theories are well understood. When one leaves the setting of one operator and considers several operators, the situation is much mo
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Functional Models for Representations of the Cuntz Algebra,le of operators on a Hilbert space. The model is determined by a weighting matrix (called a “Haplitz” matrix) which has both non-commutative Hankel and Toeplitz structure. Such positive-definite Haplitz matrices then serve to classify representations of the Cuntz algebra . with specified cyclic subs
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,On the Bessmertnyĭ Class of Homogeneous Positive Holomorphic Functions on a Product of Matrix Halfpmit representation as a Schur complement of a block of a linear homogeneous operator-valued function with positive semidefinite operator coefficients, to the case of a product of open right matrix halfplanes. Several equivalent characterizations of this generalized Bessmertnyĭ class are presented. I
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Rational Solutions of the Schlesinger System and Isoprincipal Deformations of Rational Matrix Functrticular, the isoprincipal deformations of generic rational matrix functions are proved to be isosemiresidual. The corresponding rational solutions of the Schlesinger system are constructed and the explicit expression for the related tau function is given. The main tool is the theory of joint system
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