000 03878nam a22005535i 4500
001 978-3-319-00227-9
003 DE-He213
005 20140220082506.0
007 cr nn 008mamaa
008 131115s2014 gw | s |||| 0|eng d
020 _a9783319002279
_9978-3-319-00227-9
024 7 _a10.1007/978-3-319-00227-9
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515
_223
100 1 _aBakry, Dominique.
_eauthor.
245 1 0 _aAnalysis and Geometry of Markov Diffusion Operators
_h[electronic resource] /
_cby Dominique Bakry, Ivan Gentil, Michel Ledoux.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aXX, 552 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v348
505 0 _aIntroduction -- Part I Markov semigroups, basics and examples: 1.Markov semigroups -- 2.Model examples -- 3.General setting -- Part II Three model functional inequalities: 4.Poincaré inequalities -- 5.Logarithmic Sobolev inequalities -- 6.Sobolev inequalities -- Part III Related functional, isoperimetric and transportation inequalities: 7.Generalized functional inequalities -- 8.Capacity and isoperimetry-type inequalities -- 9.Optimal transportation and functional inequalities -- Part IV Appendices: A.Semigroups of bounded operators on a Banach space -- B.Elements of stochastic calculus -- C.Some basic notions in differential and Riemannian geometry -- Notations and list of symbols -- Bibliography -- Index.
520 _aThe present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aFunctional analysis.
650 0 _aDifferential equations, partial.
650 0 _aGlobal differential geometry.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aAnalysis.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aDifferential Geometry.
650 2 4 _aPartial Differential Equations.
650 2 4 _aFunctional Analysis.
700 1 _aGentil, Ivan.
_eauthor.
700 1 _aLedoux, Michel.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319002262
830 0 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v348
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-00227-9
912 _aZDB-2-SMA
999 _c92463
_d92463