000 03450nam a22004815i 4500
001 978-3-0348-0356-4
003 DE-He213
005 20140220083254.0
007 cr nn 008mamaa
008 120717s2012 sz | s |||| 0|eng d
020 _a9783034803564
_9978-3-0348-0356-4
024 7 _a10.1007/978-3-0348-0356-4
_2doi
050 4 _aQA431
072 7 _aPBKL
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.45
_223
100 1 _aSakhnovich, Lev A.
_eauthor.
245 1 0 _aLevy Processes, Integral Equations, Statistical Physics: Connections and Interactions
_h[electronic resource] /
_cby Lev A. Sakhnovich.
264 1 _aBasel :
_bSpringer Basel :
_bImprint: Birkhäuser,
_c2012.
300 _aXX, 234 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aOperator Theory: Advances and Applications ;
_v225
505 0 _aIntroduction -- 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.
520 _aIn 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.
650 0 _aMathematics.
650 0 _aFunctional analysis.
650 0 _aIntegral equations.
650 0 _aCombinatorics.
650 1 4 _aMathematics.
650 2 4 _aIntegral Equations.
650 2 4 _aCombinatorics.
650 2 4 _aFunctional Analysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034803557
830 0 _aOperator Theory: Advances and Applications ;
_v225
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0356-4
912 _aZDB-2-SMA
999 _c101731
_d101731