Bernstein Functions

Theory and Applications
1. Auflage 2010
ISBN: 978-3-11-021530-4
Verlag: De Gruyter

Buch, Englisch, Band 37, 313 Seiten, Format (B × H): 175 mm x 246 mm, Gewicht: 737 g

Reihe: De Gruyter Studies in Mathematics

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.

Zielgruppe

Researchers, Graduate Students of Mathematics; Academic Libraries

Autoren/Hrsg.

Schilling, René L.

Vondracek, Zoran

Song, Renming

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

Frontmatter
Contents
1 Completely monotone functions
2 Stieltjes functions
3 Bernstein functions
4 Positive and negative definite functions
5 A probabilistic intermezzo
6 Complete Bernstein functions: representation
7 Complete Bernstein functions: properties
8 Thorin–Bernstein functions
9 A second probabilistic intermezzo
10 Special Bernstein functions and potentials
11 The spectral theorem and operator monotonicity
12 Subordination and Bochner’s functional calculus
13 Potential theory of subordinate killed Brownian motion
14 Applications to generalized diffusions
15 Examples of complete Bernstein functions
Backmatter

Über Autor(innen)

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