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Overview"This volume presents a systematic exposition of results hitherto only available as research articles. The recently developed theory has revealed important and fruitful connections with the theory of collective motions of systems distributed continuously in space and with the theory of algebraic curves. A rigorous mathematical definition of the physical concept of a particle is proposed, and a concrete image of a particle conceived as a localized entity in space is obtained. The duality of waves and particles then becomes a simple consequence of general equations of collective motions: particles are collective manifestations of inner states; waves are guiding waves of particles. The connection with the theory of algebraic curves is also important. For wide classes of pairs of commuting nonselfadjoint operators there exists the notion of a ""discriminant"" polynomial of two variables which generalizes the classical notion of the characteristic polynomial for a single operator. A given pair of operators annihilate their discriminant. Divisors of corresponding line bundles play the main role in the classification of commuting operators. This book is intended for researchers and postgraduate students in operator theory, system theory, quantum physics and algebraic geometry." Full Product DetailsAuthor: M.S. Livsic , N. Kravitsky , A.S. Markus , V. VinnikovPublisher: Springer Imprint: Springer Edition: 1995 ed. Volume: 332 Dimensions: Width: 15.60cm , Height: 2.00cm , Length: 23.40cm Weight: 1.440kg ISBN: 9780792335887ISBN 10: 0792335880 Pages: 318 Publication Date: 30 June 1995 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsI Operator Vessels in Hilbert Space.- 1 Preliminary Results.- 2 Colligations and Vessels.- 3 Open Systems and Open Fields.- 4 The Generalized Cayley — Hamilton Theorem.- II Joint Spectrum and Discriminant Varieties of a Commutative Vessel.- 5 Joint Spectrum and the Spectral Mapping Theorem.- 6 Joint Spectrum of Commuting Operators with Compact Imaginary Parts.- 7 Properties of Discriminant Varieties of a Commutative Vessel.- III Operator Vessels in Banach Spaces.- 8 Operator Colligations and Vessels in Banach Space.- 9 Bezoutian Vessels in Banach Space.- IV Spectral Analysis of Two-Operator Vessels.- 10 Characteristic Functions of Two-Operator Vessels in a Hilbert Space.- 11 The Determinantal Representations and the Joint Characteristic Functions in the Case of Real Smooth Cubics.- 12 Triangular Models for Commutative Two Operator Vessels on Real Smooth Cubics.- References.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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