Bernstein Functions: Theory and Applications

Description

This text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory. An extensive list of complete Bernstein functions with their representations is provided. A self-contained and unified approach to the topic With applications to various fields of mathematics, such as probability theory, potential theory, operator theory, integral equations, functional calculi and complex analysis With an extensive list of complete Bernstein functions. Additional material and corrections can be found on the authors' website. A self-contained and unified approach to the topic With applications to various fields of mathematics, such as probability theory, potential theory, operator theory, integral equations, functional calculi and complex analysis With an extensive list of complete Bernstein functions Frontmatter Contents 1 Completely monotone functions 2 Stieltjes functions 3 Bernstein functions 4 Positive and negative definite functions 5 A probabilistic intermezzo 6 Complete Bernstein functions: representation 7 Complete Bernstein functions: properties 8 Thorin–Bernstein functions 9 A second probabilistic intermezzo 10 Special Bernstein functions and potentials 11 The spectral theorem and operator monotonicity 12 Subordination and Bochner’s functional calculus 13 Potential theory of subordinate killed Brownian motion 14 Applications to generalized diffusions 15 Examples of complete Bernstein functions Backmatter