
Bernstein Functions
Theory and Applications
- 424 pages
- English
- PDF
- Available on iOS & Android
About this book
Bernstein functions appear in various fields of mathematics, e.g. probability theory, potential theory, operator theory, functional analysis and complex analysis – often with different definitions and under different names. Among the synonyms are `Laplace exponent' instead of Bernstein function, and complete Bernstein functions are sometimes called `Pick functions', `Nevanlinna functions' or `operator monotone functions'.
This monograph – now in its second revised and extended edition – offers a self-contained and unified approach to Bernstein functions and closely related function classes, bringing together old and establishing new connections. For the second edition the authors added a substantial amount of new material. As in the first edition Chapters 1 to 11 contain general material which should be accessible to non-specialists, while the later Chapters 12 to 15 are devoted to more specialized topics. An extensive list of complete Bernstein functions with their representations is provided.
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Information
Table of contents
- Preface to the second edition
- Preface
- Index of notation
- 1 Completely monotone functions
- 2 Stieltjes functions
- 3 Bernstein functions
- 4 Positive and negative definite functions
- 5 A probabilistic intermezzo
- 6 Complete Bernstein functions
- 7 Properties of complete Bernstein functions
- 8 Thorin-Bernstein functions
- 9 A second probabilistic intermezzo
- 10 Transformations of Bernstein functions
- 11 Special Bernstein functions and potentials
- 12 The spectral theorem and operator monotonicity
- 13 Subordination and Bochner’s functional calculus
- 14 Potential theory of subordinate killed Brownian motion
- 15 Applications to generalized diffusions
- 16 Examples of complete Bernstein functions
- Appendix
- Bibliography
- Index