Levy processes, integral equations, statistical physics : connections and interactions
 Author/Creator
 Sakhnovich, L. A.
 Language
 English.
 Imprint
 Basel ; London : Birkhäuser, c2012.
 Physical description
 ix, 245 p. ; 24 cm.
 Series
 Operator theory, advances and applications ; v. 225.
Access
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 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 nonfactorable 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 (Gibbstype formulas, nonextensive 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 KadisonSinger and GohbergKrein 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Lev A. Sakhnovich.
 Series
 Operator theory : advances and applications ; v. 225
 Note
 Also published electronically.
 ISBN
 9783034803557
 3034803559