Generators and their potential theory / N. Jacob.

Format:

Book

Author/Creator:

Jacob, Niels.

Series:

Jacob, Niels. Pseudo differential operators & Markov processes ; v. 2.

Pseudo differential operators & Markov processes ; v. 2

Language:

English

Subjects (All):

Semigroups of operators.

Pseudodifferential operators.

Potential theory (Mathematics).

Physical Description:

1 online resource (476 p.)

Edition:

1st ed.

Place of Publication:

London : Imperial College Press, c2002.

Language Note:

English

Summary:

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 sem

Contents:

""Contents ""; ""Preface ""; ""Notation ""; ""General Notation ""; ""Functions and Distributions ""; ""Measures and Integrals ""; ""Spaces of Functions Measures and Distributions ""; ""Some Families of Functions ""; ""Norms Scalar Products and Seminorms ""

""Notation from Functional Analysis Operators """"Notations related to Pseudo-Differential Operators ""; ""Notations related to Potential Theory and Harmonic Analysis ""; ""Introduction: Pseudo-Differential Operators and Markov Processes ""; ""II Generators and Their Potential Theory ""

""1 Introduction """"2 Generators of Feller and Sub-Markovian Semigroups ""; ""2.1 Second Order Elliptic Differential Operators as Generators of Feller and Sub-Markovian Semigroups ""

""2.2 Some Second Order Differential Operators with Non-Negative Characteristic Form as Generators of Sub-Markovian Semigroups """"2.3 Some Properties of Pseudo-Differential Operators with Negative Definite Symbols ""

""2.4 Hoh's Symbolic Calculus for Pseudo-Differential Operators with Negative Definite Symbols """"2.5 Estimates for Pseudo-Differential Operators with Negative Definite Symbols Using the Symbolic Calculus ""

""2.6 Feller Semigroups and Sub-Markovian Semigroups Generated by Pseudo-Differential Operators ""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9781860949562

1860949568

OCLC:

879025167