1.

Record Nr.

UNINA9910454270403321

Autore

Jacob Niels

Titolo

Pseudo differential operators & Markov processes . Volume 1 Fourier analysis and semigroups [[electronic resource] /] / N. Jacob

Pubbl/distr/stampa

London, : Imperial College Press

River Edge, NJ, : distributed by World Scientific, c2001

ISBN

1-281-86947-3

9786611869472

1-86094-974-6

Descrizione fisica

1 online resource (516 p.)

Disciplina

519.233

Soggetti

Fourier analysis

Pseudodifferential operators

Dirichlet forms

Markov processes

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                                                  """"Introduction: Pseudo Differential Operators and Markov Processes                                                                       ""; ""I Fourier Analysis and Semigroups                                        ""; ""1 Introduction                     ""; ""2 Essentials from Analysis                                 ""; ""2.1 Calculus Results                           ""; ""2.2 Some Topology                        ""

""2.3 Measure Theory and Integration                                         """"2.4 Convexity                    ""; ""2.5 Analytic Functions                             ""; ""2.6 Functions and Distributions                                      ""; ""2.7 Some Functional Analysis                                   ""; ""2.8 Some Interpolation



Theory                                    ""; ""3 Fourier Analysis and Convolution Semigroups                                                    ""; ""3.1 The Fourier Transform in S(Rn)                                         ""

""3.2 The Fourier Transform in Lp(Rn) 1 <p< 2                                                  """"3.3 The Fourier Transform in S'(Rn)                                          ""; ""3.4 The Paley-Wiener-Schwartz Theorem                                            ""; ""3.5 Bounded Borel Measures and Positive Definite Functions                                                                 ""; ""3.6 Convolution Semigroups and Negative Definite Functions                                                                 ""

""3.7 The Levy-Khinchin Formula for Continuous Negative Definite Functions                                                                               """"3.8 Laplace and Stieltjes Transform and Completely Monotone Functions                                                                            ""; ""3.9 Bernstein Functions and Subordination of Convolution Semigroups                                                                          ""

""3.10 Some Function Spaces related to Continuous Negative Definite Functions                                                                                  ""

Sommario/riassunto

After recalling essentials of analysis - including functional analysis, convexity, distribution theory and interpolation theory - this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students.  Sample Chapter(s)Introduction: Pseudo Differential Operators and Markov Processes