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＜E-Book＞
Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions / by Lev A. Sakhnovich
(Operator Theory: Advances and Applications. ISSN:22964878 ; 225)

Edition	1st ed. 2012.
Publisher	(Basel : Springer Basel : Imprint: Birkhäuser)
Year	2012
Language	English
Size	X, 246 p : online resource
Authors	*Sakhnovich, Lev A author SpringerLink (Online service)
Subjects	LCSH:Integral equations LCSH:Discrete mathematics LCSH:Functional analysis FREE:Integral Equations FREE:Discrete Mathematics FREE:Functional Analysis
Notes	Introduction -- 1 Levy processes -- 2 The principle of imperceptibility of the boundary -- 3 Approximation of positive functions -- 4 Optimal prediction and matched filtering -- 5 Effective construction of a class of non-factorable operators -- 6 Comparison of thermodynamic characteristics -- 7 Dual canonical systems and dual matrix string equations -- 8 Integrable operators and Canonical Differential Systems -- 9 The game between energy and entropy -- 10 Inhomogeneous Boltzmann equations -- 11 Operator Bezoutiant and concrete examples -- Comments -- Bibliography -- Glossary -- Index In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis also plays a central role in the present book. However, our approach is mainly based on the application of analysis methods (the method of operator identities, integral equations theory, dual systems, integrable equations) to probability theory (Levy processes, M. Kac's problems, the principle of imperceptibility of the boundary, signal theory). The essential part of the book is dedicated to problems of statistical physics (classical and quantum cases). We consider the corresponding statistical problems (Gibbs-type formulas, non-extensive statistical mechanics, Boltzmann equation) from the game point of view (the game between energy and entropy). One chapter is dedicated to the construction of special examples instead of existence theorems (D. Larson's theorem, Ringrose's hypothesis, the Kadison-Singer and Gohberg-Krein questions). We also investigate the Bezoutiant operator. In this context, we do not make the assumption that the Bezoutiant operator is normally solvable, allowing us to investigate the special classes of the entire functions HTTP:URL=https://doi.org/10.1007/978-3-0348-0356-4

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