Pseudo differential operators & Markov processes. Volume 1, Fourier analysis and semigroups / N. Jacob.

Format:

Book

Author/Creator:

Jacob, Niels.

Language:

English

Subjects (All):

Fourier analysis.

Pseudodifferential operators.

Dirichlet forms.

Markov processes.

Physical Description:

1 online resource (516 p.)

Edition:

1st ed.

Place of Publication:

London : Imperial College Press ; River Edge, NJ : distributed by World Scientific, c2001.

Language Note:

English

Summary:

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

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 """"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 ""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786611869472

9781281869470

1281869473

9781860949746

1860949746

OCLC:

815742426