Overview

In this volume two topics are discussed: the construction of Feller and Lp sub-Markovian semigroups by starting with a pseudo-differential operator, and the potential theory of these semigroups and their generators. The first part of the text essentially discusses the analysis of pseudo-differential operators with negative definite symbols and develops a symbolic calculus; in addition, it deals with special approaches, such as subordination in the sense of Bochner. The second part handles capacities, function spaces associated with continuous negative definite functions, Lp sub-Markovian semigroups in their associated Bessel potential spaces, Stein's Littlewood Paley theory, global properties of Lp sub-Markovian semigroups, and estimates for transition functions.Contents: Generators of Feller and Sub-Markovian Semigroups: Second Order Elliptic Differential Operators as Generators of Feller and Sub-Markovian SemigroupsSome Second Order Differential Operators with Non-Negative Characteristic Form as Generators of Sub-Markovian SemigroupsSome Properties of Pseudo-Differential Operators with Negative Definite SymbolsHoh's Symbolic Calculus for Pseudo-Differential Operators with Negative Definite SymbolsEstimates for Pseudo-Differential Operators with Negative Definite Symbols Using the Symbolic CalculusFeller Semigroups and Sub-Markovian Semigroups Generated by Pseudo-Differential OperatorsFurther Analytic Approaches for Constructing Feller and Sub-Markovian SemigroupsSome Perturbation ResultsOn Semigroups Obtained by SubordinationPseudo-Differential Operators with Variable Order of Differentiation as Generators of Feller Semigroups Potential Theory of Semigroups and Generators: Capacities and Abstract Bessel Potential SpacesFirst Results on Lp -Sub-Markovian Semigroups in their Associated Bessel Potential SpacesBessel Potential Spaces Assocated with a Continuous Negative Definite FunctionStein's Littlewood Paley Theory for Sub-Markovian SemigroupsGlobal Properties of Lp -Sub-Markovian SemigroupsNash-Type and Sobolev-Type Inequalities a Short OutlineReadership: Graduate students, lecturers and researchers in the fields of analysis & differential equations, stochastics, probability & statistics, and mathematical physics.

Full Product Details

9781299604179

Table of Contents

Reviews

Author Information

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available