LEADER 04967nam 22007695 450 001 9910299963103321 005 20200703084244.0 010 $a3-319-00227-9 024 7 $a10.1007/978-3-319-00227-9 035 $a(CKB)3710000000074643 035 $a(EBL)1593010 035 $a(SSID)ssj0001067157 035 $a(PQKBManifestationID)11551218 035 $a(PQKBTitleCode)TC0001067157 035 $a(PQKBWorkID)11079181 035 $a(PQKB)10922964 035 $a(MiAaPQ)EBC1593010 035 $a(DE-He213)978-3-319-00227-9 035 $a(PPN)176103074 035 $a(EXLCZ)993710000000074643 100 $a20131115d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnalysis and Geometry of Markov Diffusion Operators /$fby Dominique Bakry, Ivan Gentil, Michel Ledoux 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (555 p.) 225 1 $aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v348 300 $aDescription based upon print version of record. 311 $a3-319-00226-0 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThe present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic. 410 0$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v348 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aProbabilities 606 $aDifferential geometry 606 $aPartial differential equations 606 $aFunctional analysis 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aProbabilities. 615 0$aDifferential geometry. 615 0$aPartial differential equations. 615 0$aFunctional analysis. 615 14$aAnalysis. 615 24$aProbability Theory and Stochastic Processes. 615 24$aDifferential Geometry. 615 24$aPartial Differential Equations. 615 24$aFunctional Analysis. 676 $a519.233 700 $aBakry$b Dominique$4aut$4http://id.loc.gov/vocabulary/relators/aut$060682 702 $aGentil$b Ivan$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aLedoux$b Michel$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910299963103321 996 $aAnalysis and Geometry of Markov Diffusion Operators$92532458 997 $aUNINA