Schilling / Song / Vondracek Bernstein Functions

Theory and Applications
2. revidierte and ext. ed
ISBN: 978-3-11-026933-8
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 424 Seiten

Reihe: ISSN

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.

Zielgruppe

Graduate Students, Lecturers, and Researchers in Mathematics; Academic Libraries

Autoren/Hrsg.

Schilling, René L.

Song, Renming

Vondracek, Zoran

Fachgebiete

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

Inhaltsverzeichnis

1;Preface to the second edition;5
2;Preface;6
3;Index of notation;13
4;1 Completely monotone functions;15
5;2 Stieltjes functions;30
6;3 Bernstein functions;35
7;4 Positive and negative definite functions;49
8;5 A probabilistic intermezzo;62
9;6 Complete Bernstein functions;83
9.1;6.1 Representation of complete Bernstein functions;83
9.2;6.2 Extended complete Bernstein functions;94
10;7 Properties of complete Bernstein functions;106
11;8 Thorin-Bernstein functions;123
12;9 A second probabilistic intermezzo;131
13;10 Transformations of Bernstein functions;145
14;11 Special Bernstein functions and potentials;173
14.1;11.1 Special Bernstein functions;173
14.2;11.2 Hirsch’s class;186
15;12 The spectral theorem and operator monotonicity;193
15.1;12.1 The spectral theorem;193
15.2;12.2 Operator monotone functions;201
16;13 Subordination and Bochner’s functional calculus;214
16.1;13.1 Semigroups and subordination in the sense of Bochner;214
16.2;13.2 A functional calculus for generators of semigroups;230
16.3;13.3 Subordination and functional inequalities;247
16.4;13.4 Eigenvalue estimates for subordinate processes;256
17;14 Potential theory of subordinate killed Brownian motion;271
18;15 Applications to generalized diffusions;282
18.1;15.1 Inverse local time at zero;282
18.2;15.2 First passage times;299
19;16 Examples of complete Bernstein functions;313
19.1;16.1 Special functions used in the tables;314
19.2;16.2 Algebraic functions;318
19.3;16.3 Exponential functions;326
19.4;16.4 Logarithmic functions;328
19.5;16.5 Inverse trigonometric functions;344
19.6;16.6 Hyperbolic functions;344
19.7;16.7 Inverse hyperbolic functions;350
19.8;16.8 Gamma and related special functions;354
19.9;16.9 Bessel functions;364
19.10;16.10 Miscellaneous functions;372
19.11;16.11 CBFs given by exponential representations;380
19.12;16.12 Additional comments;385
20;Appendix;388
20.1;A.1 Vague and weak convergence of measures;388
20.2;A.2 Hunt processes and Dirichlet forms;391
21;Bibliography;397
22;Index;420

Über Autor(innen)

Vondracek, Zoran
Zoran Vondra?ek, University of Zagreb, Croatia.

Schilling, René L.
René L. Schilling, Dresden University of Technology, Germany;

Song, Renming
Renming Song, University of Illinois, Urbana, USA;

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