Bernstein Functions: Theory and ApplicationsWalter 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. |
Im Buch
Ergebnisse 1-5 von 48
... results and examples are scattered throughout the literature ; the exceedingly rich structure connecting this material got lost in the process . Our motivation for writing this book was to point out many of these connections and to ...
... results in the theory of generalized diffusions , both related to complete Bernstein functions through Krein's theory of strings . Many of these results appear for the first time in a monograph . The third part of the book is formed by ...
... result Corollary 1.8 seems to be new. Definition 1.10 and the results on multiply monotone functions are from [372], our proofs are adaptations of [317, Chapter 2]. The connection between complete mono- tonicity and complete ...
... result ( 7.2 ) in Chapter 7 below shows that { F } = S. In his paper [ 162 ] F. Hirsch introduces Stieltjes transforms into potential theory and identifies S as a convex cone operating on the abstract potentials , i.e. the densely ...
... result is due to Srivastava and Tuan [335]: if f 2 Lp.0;1/ and g 2 Lq.0;1/ with 1 < p;q < 1 and r 1 D p 1 C q 1 < 1, then there is some h 2 Lr.0;1/ such that 多 2.f I /多 2.gI / D 多 2.hI / holds. Since Z Z 1 1 0 f .u/ h.t/ D f.t/ p.v. ...
Inhalt
1 | |
16 | |
21 | |
35 | |
48 | |
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 |
Index | 406 |
Andere Ausgaben - Alle anzeigen
Bernstein Functions: Theory and Applications René L. Schilling,Renming Song,Zoran Vondraček Keine Leseprobe verfügbar - 2010 |
Bernstein Functions: Theory and Applications René L. Schilling,Renming Song,Zoran Vondraček Keine Leseprobe verfügbar - 2012 |
Bernstein Functions: Theory and Applications René L. Schilling,Renming Song,Zoran Vondraček Keine Leseprobe verfügbar - 2012 |