1.

Record Nr.

UNINA9910451919203321

Autore

Jacob Niels

Titolo

Generators and their potential theory [[electronic resource] /] / N. Jacob

Pubbl/distr/stampa

London, : Imperial College Press, c2002

ISBN

1-86094-956-8

Descrizione fisica

1 online resource (476 p.)

Collana

Pseudo differential operators & Markov processes ; ; v. 2

Disciplina

519.233

Soggetti

Semigroups of operators

Pseudodifferential operators

Potential theory (Mathematics)

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

""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                                                                                                    ""

Sommario/riassunto

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