Analysis and Geometry of Markov Diffusion Operators

• Κύριοι συγγραφείς: Bakry, Dominique (Συγγραφέας), Gentil, Ivan (Συγγραφέας), Ledoux, Michel (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Σειρά: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 348
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Functional analysis.; Partial differential equations.; Differential geometry.; Probabilities.; Analysis.; Probability Theory and Stochastic Processes.; Differential Geometry.; Partial Differential Equations.; Functional Analysis.

The 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, Sobo...

Πίνακας περιεχομένων:

• Introduction
• 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.