Bernstein Functions

René L. Schilling; Renming Song; Zoran Vondracek

Published by De Gruyter 2010

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/10.1515/9783110215311

Overview
Contents

About this book

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

Author information

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

Frontmatter Requires Authentication Accessible PDF	i
Contents Requires Authentication Accessible PDF	v
1 Completely monotone functions Requires Authentication Accessible PDF	1
2 Stieltjes functions Requires Authentication Accessible PDF	11
3 Bernstein functions Requires Authentication Accessible PDF	15
4 Positive and negative definite functions Requires Authentication Accessible PDF	25
5 A probabilistic intermezzo Requires Authentication Accessible PDF	34
6 Complete Bernstein functions: representation Requires Authentication Accessible PDF	49
7 Complete Bernstein functions: properties Requires Authentication Accessible PDF	62
8 Thorin–Bernstein functions Requires Authentication Accessible PDF	73
9 A second probabilistic intermezzo Requires Authentication Accessible PDF	80
10 Special Bernstein functions and potentials Requires Authentication Accessible PDF	92
11 The spectral theorem and operator monotonicity Requires Authentication Accessible PDF	110
12 Subordination and Bochner’s functional calculus Requires Authentication Accessible PDF	130
13 Potential theory of subordinate killed Brownian motion Requires Authentication Accessible PDF	174
14 Applications to generalized diffusions Requires Authentication Accessible PDF	185
15 Examples of complete Bernstein functions Requires Authentication Accessible PDF	214
Backmatter Requires Authentication Accessible PDF	281

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers, Graduate Students of Mathematics; Academic Libraries
Pages
- Front matter: 11
- Main content: 313
Illustrations
- Illustrations: 3
Keywords: Bernstein Functions; Complete Bernstein Functions; Completely Monotone Function; Stieltjes Function/Transform; Laplace Transform

eBook

Published: December 22, 2009
ISBN: 9783110215311

Hardcover

Published: January 14, 2010
ISBN: 9783110215304