by N Jacob (University of Wales Swansea, UK)

Contents (136k)
Preface (71k)
Introduction: Pseudo Differential Operators and Markov Processes (207k)
Chapter 1: Introduction (190k)

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.

• Essentials from Analysis:
  • Calculus Results
  • Convexity
  • Some Interpolation Theory
• Fourier Analysis and Convolution Semigroups:
  • The Paley–Wiener–Schwartz Theorem
  • Bounded Borel Measures and Positive Definite Functions
  • Convolution Semigroups and Negative Definite Functions
  • The Lévy–Khinchin Formula for Continuous Negative Definite Functions
  • Bernstein Functions and Subordination of Convolution Semigroups
  • Fourier Multiplier Theorems
• One Parameter Semigroups:
  • Strongly Continuous Operator Semigroups
  • Subordination in the Sense of Bochner for Operator Semigroups
  • Generators of Feller Semigroups
  • Dirichlet Forms and Generators of Sub-Markovian Semigroups
  • and other papers