Bernstein Functions Theory and Applications 1st Edition by René Schilling, Renming Song, Zoran Vondracek 9783110215311 3110215314
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Product details:
ISBN 10: 3110215314
ISBN 13: 9783110215311
Author: René L. Schilling; Renming Song; Zoran Vondracek
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.
Table of 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
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Tags: René Schilling, Renming Song, Zoran Vondracek, Bernstein