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ISBN: 0792335880
ID: 4171784854
[EAN: 9780792335887], [PU: SPNL], Brand NEW unread book. This item is printed on demand. Perfectly bound book in mint condition. This hard cover print on demand book can incur an additional 1-2 working days handling time on top of the regular 2-3 working day delivery for UK standard delivery. Please note expedited shipping does not accelerate delivery times for print on demand books. We ship using Royal Mail or courier in the UK and Europe with tracking number for heavier or more valuable items. All USA orders have a shipment tracking number.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.Preface. Introduction. I: 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. Index.
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ISBN: 9780792335887
ID: 6385545
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. 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. Books, Science and Geography~~Mathematics~~Calculus & Mathematical Analysis, Theory Of Commuting Nonselfadjoint Operators~~Book~~9780792335887~~M.S. Livsic, A.S Markus, V. Vinnikov, , , , , , , , , ,, [PU: Kluwer Academic Publishers]
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1995
ISBN: 0792335880
Lieferbar binnen 4-6 Wochen
ID: 9780792335887
In englischer Sprache. Verlag: Springer-Verlag GmbH, HC runder Rücken kaschiert, 340 Seiten, L=235mm, B=155mm, H=23mm, Gew.=672gr, [GR: 16200 - HC/Mathematik], [SW: - Algebraische Geometrie], Gebunden, Klappentext: 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.
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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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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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Titre: | Theory of Commuting Nonselfadjoint Operators |
ISBN: | 9780792335887 |
Informations détaillées sur le livre - Theory of Commuting Nonselfadjoint Operators
EAN (ISBN-13): 9780792335887
ISBN (ISBN-10): 0792335880
Version reliée
Date de parution: 1995
Editeur: Springer-Verlag GmbH
340 Pages
Poids: 0,672 kg
Langue: eng/Englisch
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Livre trouvé récemment le 25.12.2015 14:19:03
ISBN/EAN: 9780792335887
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