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. |
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... semigroup .Œ0;1/;C/. This justifies the name Lévy measure and Lévy triplet for and .a; b; /, respectively; this point of view is taken in [38]. The representation (3.4) is taken from Prüss [297, Chapter I.4.1] who calls the functions ...
... semigroup with involution .S;C; / is a nonempty set equipped with a commutative and associative addition C, a zero ... semigroups .Œ0;1/;C/ and .Rd;C/ where 'C' is the usual addition; the respective involutions are the identity mapping s ...
... semigroup .Œ0;1/;C/ with involution D ; it will turn out that these functions coincide with the families CM b and BF, respectively. Since we are working on the closed half-line Œ0;1/, it is useful to extend f 2 CMb or f 2 BF ...
... semigroups is due to Ressel [302] and Berg, Christensen and Ressel [37]. Ressel observes that positive definiteness (in a semigroup sense) establishes the connection between two seemingly different topics: Fourier transforms and ...
... semigroup of. holds for every compactly supported continuous function ƒ : [ 0 , ∞ ) → R , see Ap- pendix A.1 . The convolution of the sub - probability measures μ and v on [ 0 , ∞ ) is defined to be the sub - probability measure μ ...
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 |