Bernstein Functions: Theory and Applications

René L. Schilling; Renming Song; Zoran Vondracek

Published by De Gruyter 2012

Bernstein Functions

Theory and Applications

René L. Schilling , Renming Song and Zoran Vondracek

Volume 37 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110269338

Overview
Contents

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.

Author / Editor information

René L. Schilling, Dresden University of Technology, Germany; Renming Song, University of Illinois, Urbana, USA; Zoran Vondraček, University of Zagreb, Croatia.

Reviews

"To sum up, the book collects and integrates results from a number of sources scattered throughout the literature. It is clearly and carefully written. It will certainly be useful for both graduate students and researchers in different areas." Mathematical Reviews (review of the first edition)

"This impressive monograph, which is now in an expanded second edition, does a wonderful job of collecting together and synthesising some of the most important results and applications. Consequently it represents a unique perspective on this important function class which will be a valuable resource for many years to come for both experienced researchers and graduate students." Mathematical Reviews

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	i
Preface to the second edition Requires Authentication Unlicensed Licensed Download PDF	v
Preface Requires Authentication Unlicensed Licensed Download PDF	vi
Contents Requires Authentication Unlicensed Licensed Download PDF	xi
Index of notation Requires Authentication Unlicensed Licensed Download PDF	xiii
Chapter 1. Laplace transforms and completely monotone functions Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 2. Stieltjes functions Requires Authentication Unlicensed Licensed Download PDF	16
Chapter 3. Bernstein functions Requires Authentication Unlicensed Licensed Download PDF	21
Chapter 4. Positive and negative definite functions Requires Authentication Unlicensed Licensed Download PDF	35
Chapter 5. A probabilistic intermezzo Requires Authentication Unlicensed Licensed Download PDF	48
Chapter 6. Complete Bernstein functions Requires Authentication Unlicensed Licensed Download PDF	69
Chapter 7. Properties of complete Bernstein functions Requires Authentication Unlicensed Licensed Download PDF	92
Chapter 8. Thorin–Bernstein functions Requires Authentication Unlicensed Licensed Download PDF	109
Chapter 9. A second probabilistic intermezzo Requires Authentication Unlicensed Licensed Download PDF	117
Chapter 10. Transformations of Bernstein functions Requires Authentication Unlicensed Licensed Download PDF	131
Chapter 11. Special Bernstein functions and potentials Requires Authentication Unlicensed Licensed Download PDF	159
Chapter 12. The spectral theorem and operator monotonicity Requires Authentication Unlicensed Licensed Download PDF	179
Chapter 13. Subordination and Bochner’s functional calculus Requires Authentication Unlicensed Licensed Download PDF	200
Chapter 14. Potential theory of subordinate killed Brownian motion Requires Authentication Unlicensed Licensed Download PDF	257
Chapter 15. Applications to generalized diffusions Requires Authentication Unlicensed Licensed Download PDF	268
Chapter 16. Examples of complete Bernstein functions Requires Authentication Unlicensed Licensed Download PDF	299
Appendix Requires Authentication Unlicensed Licensed Download PDF	374
Bibliography Requires Authentication Unlicensed Licensed Download PDF	383
Index Requires Authentication Unlicensed Licensed Download PDF	406

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: 2nd rev. and ext. ed.
Audience: Graduate Students, Lecturers, and Researchers in Mathematics; Academic Libraries
Pages
- Front matter: 14
- Main content: 410
Illustrations
- Illustrations: 5
- Tables: 10
Keywords: Bernstein Function; Monotone Function; Probability Measure; Semigroup; Theory

eBook

Published: October 1, 2012
ISBN: 9783110269338

Hardcover

Published: September 14, 2012
ISBN: 9783110252293