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Autore: |
Schilling René L
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Titolo: |
Bernstein functions [[electronic resource] ] : theory and applications / / by Rene L. Schilling, Renming Song, Zoran Vondracek
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Pubblicazione: | Berlin, : De Gruyter, c2012 |
Edizione: | 2nd ed. |
Descrizione fisica: | 1 online resource (424 p.) |
Disciplina: | 515/.8 |
Soggetto topico: | Analytic functions |
Monotonic functions | |
Quasianalytic functions | |
Soggetto non controllato: | Bernstein Function |
Monotone Function | |
Probability Measure | |
Semigroup | |
Theory | |
Classificazione: | SK 420 |
Altri autori: |
SongRenming <1963->
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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. |
Titolo autorizzato: | Bernstein functions ![]() |
ISBN: | 3-11-026900-7 |
1-283-85675-1 | |
Formato: | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910786435503321 |
Lo trovi qui: | Univ. Federico II |
Opac: | Controlla la disponibilità qui |