Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators

• Κύριος συγγραφέας: Eberle, Andreas (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999.
• Έκδοση: 1st ed. 1999.
• Σειρά: Lecture Notes in Mathematics, 1718
• Θέματα: Probabilities.; Partial differential equations.; Group theory.; Potential theory (Mathematics).; Probability Theory and Stochastic Processes.; Partial Differential Equations.; Group Theory and Generalizations.; Potential Theory.

 This book addresses both probabilists working on diffusion processes and analysts interested in linear parabolic partial differential equations with singular coefficients. The central question discussed is whether a given diffusion operator, i.e., a second order linear differential operator without zeroth order term, which is a priori defined on test functions over some (finite or infinite dimensional) state space only, uniquely determines a strongly continuous semigroup on a corresponding weighted Lp space. Particular emphasis is placed on phenomena causing non-uniqueness, as well as on the relation between different notions of uniqueness appearing in analytic and probabilistic contexts. 

 Motivation and basic definitions: Uniqueness problems in various contexts -- L p uniqueness in finite dimensions -- Markov uniqueness -- Probabilistic aspects of L p and Markov uniqueness -- First steps in infinite dimensions.