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Other titles in the Operator Theory: Advances and Applications series:

Operator Theory: Advances and Applications #225: Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions

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Operator Theory: Advances and Applications #225: Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This book explores the interconnection of probability and analysis, in an approach mainly based on the application of analysis methods to probability theory. Among many concepts, the authors address problems of statistical physics from the game point of view.

Table of Contents

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.

Product Details

ISBN:
9783034803557
Author:
Sakhnovich, Lev A.
Publisher:
Birkhauser
Location:
Basel
Subject:
Mathematical Analysis
Subject:
Lâevy processes.
Subject:
Energy
Subject:
Entropy
Subject:
stable processes
Subject:
triangular factorization
Subject:
Integral equations
Subject:
Combinatorics
Subject:
Functional Analysis
Subject:
Mathematics-Analysis General
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Copyright:
Edition Description:
2012
Series:
Operator Theory: Advances and Applications
Series Volume:
225
Publication Date:
20120727
Binding:
HARDCOVER
Language:
English
Pages:
256
Dimensions:
235 x 155 mm

Related Subjects


Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Combinatorics
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Modeling
Science and Mathematics » Physics » General

Operator Theory: Advances and Applications #225: Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions New Hardcover
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$118.50 In Stock
Product details 256 pages Birkh User - English 9783034803557 Reviews:
"Synopsis" by , This book explores the interconnection of probability and analysis, in an approach mainly based on the application of analysis methods to probability theory. Among many concepts, the authors address problems of statistical physics from the game point of view.
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