Bernstein functions [[electronic resource] ] : theory and applications / / by Rene L. Schilling, Renming Song, Zoran Vondracek

• Record Nr.: UNINA9910462980303321
• Autore: Schilling René L
• Pubbl/distr/stampa: Berlin, : De Gruyter, c2012
• ISBN: 3-11-026900-7; 1-283-85675-1
• Edizione: [2nd ed.]
• Descrizione fisica: 1 online resource (424 p.)
• Collana: De Gruyter Studies in Mathematics ; ; 37
• Altri autori (Persone): SongRenming <1963->; VondračekZoran <1959->
• Disciplina: 515/.8
• Soggetti: Analytic functions; Monotonic functions; Quasianalytic functions; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. [383]-) and index.
• Nota di contenuto: Front matter -- Preface to the second edition -- Preface -- Contents -- Index of notation -- Chapter 1. Laplace transforms and completely monotone functions -- Chapter 2. Stieltjes functions -- Chapter 3. Bernstein functions -- Chapter 4. Positive and negative definite functions -- Chapter 5. A probabilistic intermezzo -- Chapter 6. Complete Bernstein functions -- Chapter 7. Properties of complete Bernstein functions -- Chapter 8. Thorin-Bernstein functions -- Chapter 9. A second probabilistic intermezzo -- Chapter 10. Transformations of Bernstein functions -- Chapter 11. Special Bernstein functions and potentials -- Chapter 12. The spectral theorem and operator monotonicity -- Chapter 13. Subordination and Bochner's functional calculus -- Chapter 14. Potential theory of subordinate killed Brownian motion -- Chapter 15. Applications to generalized diffusions -- Chapter 16. Examples of complete Bernstein functions -- Appendix -- Bibliography -- Index
• Sommario/riassunto: 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.