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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,...
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| Main Authors: | |
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| Corporate Authors: | |
| Group Author: | ; |
| Published: |
De Gruyter,
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| Publisher Address: | Berlin : |
| Publication Dates: | [2012] |
| Literature type: | eBook |
| Language: | English |
| Edition: | 2nd rev. and ext. ed. |
| Series: |
De gruyter studies in mathematics ;
37 |
| Subjects: | |
| Online Access: |
http://dx.doi.org/10.1515/9783110269338 http://www.degruyter.com/doc/cover/9783110269338.jpg |
| Summary: |
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. |
| Carrier Form: | 1 online resource (424 pages). |
| ISBN: | 9783110269338（electronic bk.） |
| Index Number: | QA331 |
| CLC: | O174 |
| Contents: |
Frontmatter -- Preface to the second edition -- Preface -- Contents -- Index of notation -- Chapter 1. Laplace transforms and completely monotone functions -- Chapter 2. Stieltjes functions -- Chapter 3. Bernstein functions -- Chapter 4. Positive and negative definite functions -- Chapter 5. A probabilistic intermezzo -- Chapter 6. Complete Bernstein functions -- Chapter 7. Properties of complete Bernstein functions -- Chapter 8. Thorin Bernstein functions -- Chapter 9. A second probabilistic intermezzo -- Chapter 10. Transformations of Bernstein functions -- Chapter 11. Special Bernstein functions and potentials -- Chapter 12. The spectral theorem and operator monotonicity -- Chapter 13. Subordination and Bochner s functional calculus -- Chapter 14. Potential theory of subordinate killed Brownian motion -- Chapter 15. Applications to generalized diffusions -- Chapter 16. Examples of complete Bernstein functions -- Appendix -- Bibliography -- Index |