A.S. Sipin's Books

Random Processes for Classical Equations of Mathematical Physics

By: S.M. Ermakov,V.V. Nekrutkin,A.S. Sipin

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Random Processes for Classical Equations of Mathematical Physics

By: S.M. Ermakov,V.V. Nekrutkin,A.S. Sipin

Et moi - ... si j'avait su comment en revenir. One service mathema tics has rendered the je n'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

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301

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Springer Science & Business Media

Published Date

ISBN 10

9400922434

ISBN 13

9789400922433

Theory of Commuting Nonselfadjoint Operators

By: M.S. Livsic,N. Kravitsky,A.S. Markus,V. Vinnikov

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Theory of Commuting Nonselfadjoint Operators

By: M.S. Livsic,N. Kravitsky,A.S. Markus,V. Vinnikov

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.

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329

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Springer Science & Business Media

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ISBN 10

940158561X

ISBN 13

9789401585613

Random Processes for Classical Equations of Mathematical Physics

By: S.M. Ermakov,V.V. Nekrutkin,A.S. Sipin

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Random Processes for Classical Equations of Mathematical Physics

By: S.M. Ermakov,V.V. Nekrutkin,A.S. Sipin

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

301

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9400922434

ISBN 13

9789400922433

Book's by A.S. Sipin

Random Processes for Classical Equations of Mathematical Physics

Random Processes for Classical Equations of Mathematical Physics

Theory of Commuting Nonselfadjoint Operators

Theory of Commuting Nonselfadjoint Operators

Random Processes for Classical Equations of Mathematical Physics

Random Processes for Classical Equations of Mathematical Physics

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