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Theory of Commuting Nonselfadjoint Operators - V. Vinnikov#A. S. Markus#M. S. Livsic#N. Kravitsky
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V. Vinnikov#A. S. Markus#M. S. Livsic#N. Kravitsky:
Theory of Commuting Nonselfadjoint Operators - new book

ISBN: 9780792335887

ID: 637604924

Considering integral transformations of Volterra type, F. Riesz and B. Sz.-Nagy no­ ticed in 1952 that [49]: ´´The existence of such a variety of linear transformations, having the same spectrum concentrated at a single point, brings out the difficulties of characterization of linear transformations of general type by means of their spectra.´´ Subsequently, spectral analysis has been developed for different classes of non­ selfadjoint operators [6,7,14,20,21,36,44,46,54]. It was then realized that this analysis forms a natural basis for the theory of systems interacting with the environment. The success of this theory in the single operator case inspired attempts to create a general theory in the much more complicated case of several commuting operators with finite-dimensional imaginary parts. During the past 10-15 years such a theory has been developed, yielding fruitful connections with algebraic geometry and sys­ tem theory. Our purpose in this book is to formulate the basic problems appearing in this theory and to present its main results. It is worth noting that, in addition to the joint spectrum, the corresponding algebraic variety and its global topological characteristics play an important role in the classification of commuting operators. For the case of a pair of operators these are: 1. The corresponding algebraic curve, and especially its genus. 2. Certain classes of divisors - or certain line bundles - on this curve. Theory of Commuting Nonselfadjoint Operators Bücher > Fremdsprachige Bücher > Englische Bücher gebundene Ausgabe 30.06.1995 Buch (fremdspr.), Springer, .199

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Theory of Commuting Nonselfadjoint Operators - N. Kravitsky#M. S. Livsic#A. S. Markus#V. Vinnikov
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N. Kravitsky#M. S. Livsic#A. S. Markus#V. Vinnikov:
Theory of Commuting Nonselfadjoint Operators - new book

ISBN: 9780792335887

ID: 27167920c288c3f1c983dac09c6c20e5

Theory of Commuting Nonselfadjoint Operators Considering integral transformations of Volterra type, F. Riesz and B. Sz.-Nagy no­ ticed in 1952 that [49]: "The existence of such a variety of linear transformations, having the same spectrum concentrated at a single point, brings out the difficulties of characterization of linear transformations of general type by means of their spectra." Subsequently, spectral analysis has been developed for different classes of non­ selfadjoint operators [6,7,14,20,21,36,44,46,54]. It was then realized that this analysis forms a natural basis for the theory of systems interacting with the environment. The success of this theory in the single operator case inspired attempts to create a general theory in the much more complicated case of several commuting operators with finite-dimensional imaginary parts. During the past 10-15 years such a theory has been developed, yielding fruitful connections with algebraic geometry and sys­ tem theory. Our purpose in this book is to formulate the basic problems appearing in this theory and to present its main results. It is worth noting that, in addition to the joint spectrum, the corresponding algebraic variety and its global topological characteristics play an important role in the classification of commuting operators. For the case of a pair of operators these are: 1. The corresponding algebraic curve, and especially its genus. 2. Certain classes of divisors - or certain line bundles - on this curve. Bücher / Fremdsprachige Bücher / Englische Bücher 978-0-7923-3588-7, Springer

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Theory of Commuting Nonselfadjoint Operators - V. Vinnikov#A. S. Markus#M. S. Livsic#N. Kravitsky
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V. Vinnikov#A. S. Markus#M. S. Livsic#N. Kravitsky:
Theory of Commuting Nonselfadjoint Operators - new book

ISBN: 9780792335887

ID: 661643874

Considering integral transformations of Volterra type, F. Riesz and B. Sz.-Nagy no­ ticed in 1952 that [49]: ´´The existence of such a variety of linear transformations, having the same spectrum concentrated at a single point, brings out the difficulties of characterization of linear transformations of general type by means of their spectra.´´ Subsequently, spectral analysis has been developed for different classes of non­ selfadjoint operators [6,7,14,20,21,36,44,46,54]. It was then realized that this analysis forms a natural basis for the theory of systems interacting with the environment. The success of this theory in the single operator case inspired attempts to create a general theory in the much more complicated case of several commuting operators with finite-dimensional imaginary parts. During the past 10-15 years such a theory has been developed, yielding fruitful connections with algebraic geometry and sys­ tem theory. Our purpose in this book is to formulate the basic problems appearing in this theory and to present its main results. It is worth noting that, in addition to the joint spectrum, the corresponding algebraic variety and its global topological characteristics play an important role in the classification of commuting operators. For the case of a pair of operators these are: 1. The corresponding algebraic curve, and especially its genus. 2. Certain classes of divisors - or certain line bundles - on this curve. Theory of Commuting Nonselfadjoint Operators Buch (fremdspr.) Bücher>Fremdsprachige Bücher>Englische Bücher, Springer

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Theory of Commuting Nonselfadjoint Operators - N. Kravitsky#M. S. Livsic#A. S. Markus#V. Vinnikov
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N. Kravitsky#M. S. Livsic#A. S. Markus#V. Vinnikov:
Theory of Commuting Nonselfadjoint Operators - new book

ISBN: 9780792335887

ID: 159574507

Considering integral transformations of Volterra type, F. Riesz and B. Sz.-Nagy no­ ticed in 1952 that [49]: ´´The existence of such a variety of linear transformations, having the same spectrum concentrated at a single point, brings out the difficulties of characterization of linear transformations of general type by means of their spectra.´´ Subsequently, spectral analysis has been developed for different classes of non­ selfadjoint operators [6,7,14,20,21,36,44,46,54]. It was then realized that this analysis forms a natural basis for the theory of systems interacting with the environment. The success of this theory in the single operator case inspired attempts to create a general theory in the much more complicated case of several commuting operators with finite-dimensional imaginary parts. During the past 10-15 years such a theory has been developed, yielding fruitful connections with algebraic geometry and sys­ tem theory. Our purpose in this book is to formulate the basic problems appearing in this theory and to present its main results. It is worth noting that, in addition to the joint spectrum, the corresponding algebraic variety and its global topological characteristics play an important role in the classification of commuting operators. For the case of a pair of operators these are: 1. The corresponding algebraic curve, and especially its genus. 2. Certain classes of divisors - or certain line bundles - on this curve. Theory of Commuting Nonselfadjoint Operators Buch (fremdspr.) Bücher>Fremdsprachige Bücher>Englische Bücher, Springer

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Theory of Commuting Nonselfadjoint Operators - M.S. Livsic, N. Kravitsky, A.S. Markus
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M.S. Livsic, N. Kravitsky, A.S. Markus:
Theory of Commuting Nonselfadjoint Operators - new book

ISBN: 9780792335887

ID: 978079233588

Theory of Commuting Nonselfadjoint Operators presents a systematic and cogent 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 localised 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 generalises 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. Audience: Researchers and postgraduate students in operator theory, system theory, quantum physics and algebraic geometry. M.S. Livsic, N. Kravitsky, A.S. Markus, Books, Science and Nature, Theory of Commuting Nonselfadjoint Operators Books>Science and Nature, Springer Netherlands

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Details of the book
Theory of Commuting Nonselfadjoint Operators

Theory of Commuting Nonselfadjoint Operators presents a systematic and cogent 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 localised 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 generalises 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. Audience: Researchers and postgraduate students in operator theory, system theory, quantum physics and algebraic geometry.

Details of the book - Theory of Commuting Nonselfadjoint Operators


EAN (ISBN-13): 9780792335887
ISBN (ISBN-10): 0792335880
Hardcover
Publishing year: 1995
Publisher: Springer-Verlag GmbH
340 Pages
Weight: 0,672 kg
Language: eng/Englisch

Book in our database since 10.04.2008 11:54:18
Book found last time on 12.03.2017 09:10:21
ISBN/EAN: 0792335880

ISBN - alternate spelling:
0-7923-3588-0, 978-0-7923-3588-7


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