Bernstein Functions : : Theory and Applications / / René L. Schilling, Renming Song, Zoran Vondracek.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package
• VerfasserIn: Schilling, René L.,; Song, Renming,; Vondracek, Zoran,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2012]; ©2012
• Year of Publication: 2012
• Edition: 2nd rev. and ext. ed.
• Language: English
• Series: De Gruyter Studies in Mathematics , 37
• Physical Description: 1 online resource (410 p.)

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.

Table of 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