05276nam 2200685Ia 450 991081675280332120240404151945.01-281-86947-397866118694721-86094-974-6(CKB)1000000000537738(EBL)1681293(OCoLC)815742426(SSID)ssj0000229839(PQKBManifestationID)11947189(PQKBTitleCode)TC0000229839(PQKBWorkID)10177146(PQKB)10842670(MiAaPQ)EBC1681293(WSP)0000P245(Au-PeEL)EBL1681293(CaPaEBR)ebr10255621(EXLCZ)99100000000053773820020329d2001 uy 0engur|n|---|||||txtccrPseudo differential operators & Markov processesVolume 1Fourier analysis and semigroups /N. Jacob1st ed.London Imperial College Press ;River Edge, NJ distributed by World Scientificc20011 online resource (516 p.)Description based upon print version of record.1-86094-293-8 Includes bibliographical references and index.""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 "" 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 Fourier analysisPseudodifferential operatorsDirichlet formsMarkov processesFourier analysis.Pseudodifferential operators.Dirichlet forms.Markov processes.519.233Jacob Niels67291MiAaPQMiAaPQMiAaPQBOOK9910816752803321Pseudo differential operators & Markov processes147332UNINA