Bernstein Functions: Theory and Applications

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Walter de Gruyter, 01.10.2012 - 424 Seiten

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.

 

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Inhalt

1 Completely monotone functions
1
2 Stieltjes functions
16
3 Bernstein functions
21
4 Positive and negative definite functions
35
5 A probabilistic intermezzo
48
6 Complete Bernstein functions
69
7 Properties of complete Bernstein functions
92
8 ThorinBernstein functions
109
11 Special Bernstein functions and potentials
159
12 The spectral theorem and operator monotonicity
179
13 Subordination and Bochners functional calculus
200
14 Potential theory of subordinate killed Brownian motion
257
15 Applications to generalized diffusions
268
16 Examples of complete Bernstein functions
299
Appendix
374
Bibliography
383

9 A second probabilistic intermezzo
117
10 Transformations of Bernstein functions
131

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Über den Autor (2012)

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

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