Bernstein Functions Theory and Applications
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The wor...
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| Format: | E-Book Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin/Boston
De Gruyter
2012
Walter de Gruyter GmbH |
| Ausgabe: | 1 |
| Schriftenreihe: | De Gruyter Studies in Mathematics |
| Schlagworte: | |
| ISBN: | 9783110269338, 3110269333, 3110252295, 9783110252293, 3110215314, 9783110215311, 3110215306, 9783110215304 |
| Online-Zugang: | Volltext |
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| Abstract | The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. |
|---|---|
| AbstractList | This secondrevised andextendededition of the self-contained and unified approach to Bernstein functions and their subclassesbrings together old and establishs new connections. Applications of Bernstein functions in different fields of mathematics (such as probability theory, potential theory, operator theory, integral equations, functional calculi, and complex analysis) are given, with special attention to interpretations in probability theory. An extensive list of complete Bernstein functions with their representations is provided. The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. This text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory. An extensive list of complete Bernstein functions with their representations is provided. This text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory. An extensive list of complete Bernstein functions with their representations is provided. * A self-contained and unified approach to the topic * With applications to various fields of mathematics, such as probability theory, potential theory, operator theory, integral equations, functional calculi and complex analysis * With an extensive list of complete Bernstein functions. * Additional material and corrections can be found on the authors' website [http://www.motapa.de/bernstein_functions]. This text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory. An extensive list of complete Bernstein functions with their representations is provided. A self-contained and unified approach to the topic With applications to various fields of mathematics, such as probability theory, potential theory, operator theory, integral equations, functional calculi and complex analysis With an extensive list of complete Bernstein functions. Additional material and corrections can be found on the authors' website. |
| Author | Song, Renming Vondracek, Zoran Schilling, René L |
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| Edition | 1 2 2nd edition. |
| Editor | Song, Renming Vondracek, Zoran |
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| Keywords | Bernstein-Funktion Bernstein Functions Complete Bernstein Functions Operatortheorie Wahrscheinlichkeitsmaß Completely Monotone Function monotone Funktion Laplace Transform Stieltjes Function/Transform Halbgruppe |
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| Notes | Includes bibliographical reference (p. [383]-405) and index |
| OCLC | 651047685 820121236 |
| PQID | EBC511800 |
| PageCount | 324 pages |
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| Snippet | This text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections.... The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from... This secondrevised andextendededition of the self-contained and unified approach to Bernstein functions and their subclassesbrings together old and establishs... |
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| SubjectTerms | Analytic functions Bernstein Functions Bernstein-Funktion Complete Bernstein Functions Completely Monotone Function Halbgruppe Laplace Transform MATHEMATICS MATHEMATICS / General MATHEMATICS / Mathematical Analysis MATHEMATICS / Probability & Statistics / General Mathematics. Analysis monotone Funktion Monotonic functions Operatortheorie Quasianalytic functions Stieltjes Function/Transform Wahrscheinlichkeitsmaß |
| Subtitle | Theory and Applications |
| TableOfContents | Frontmatter -- Contents -- 1 Completely monotone functions -- 2 Stieltjes functions -- 3 Bernstein functions -- 4 Positive and negative definite functions -- 5 A probabilistic intermezzo -- 6 Complete Bernstein functions: representation -- 7 Complete Bernstein functions: properties -- 8 Thorin-Bernstein functions -- 9 A second probabilistic intermezzo -- 10 Special Bernstein functions and potentials -- 11 The spectral theorem and operator monotonicity -- 12 Subordination and Bochner's functional calculus -- 13 Potential theory of subordinate killed Brownian motion -- 14 Applications to generalized diffusions -- 15 Examples of complete Bernstein functions -- Backmatter Intro -- Preface to the second edition -- Preface -- Index of notation -- 1 Completely monotone functions -- 2 Stieltjes functions -- 3 Bernstein functions -- 4 Positive and negative definite functions -- 5 A probabilistic intermezzo -- 6 Complete Bernstein functions -- 6.1 Representation of complete Bernstein functions -- 6.2 Extended complete Bernstein functions -- 7 Properties of complete Bernstein functions -- 8 Thorin-Bernstein functions -- 9 A second probabilistic intermezzo -- 10 Transformations of Bernstein functions -- 11 Special Bernstein functions and potentials -- 11.1 Special Bernstein functions -- 11.2 Hirsch's class -- 12 The spectral theorem and operator monotonicity -- 12.1 The spectral theorem -- 12.2 Operator monotone functions -- 13 Subordination and Bochner's functional calculus -- 13.1 Semigroups and subordination in the sense of Bochner -- 13.2 A functional calculus for generators of semigroups -- 13.3 Subordination and functional inequalities -- 13.4 Eigenvalue estimates for subordinate processes -- 14 Potential theory of subordinate killed Brownian motion -- 15 Applications to generalized diffusions -- 15.1 Inverse local time at zero -- 15.2 First passage times -- 16 Examples of complete Bernstein functions -- 16.1 Special functions used in the tables -- 16.2 Algebraic functions -- 16.3 Exponential functions -- 16.4 Logarithmic functions -- 16.5 Inverse trigonometric functions -- 16.6 Hyperbolic functions -- 16.7 Inverse hyperbolic functions -- 16.8 Gamma and related special functions -- 16.9 Bessel functions -- 16.10 Miscellaneous functions -- 16.11 CBFs given by exponential representations -- 16.12 Additional comments -- Appendix -- A.1 Vague and weak convergence of measures -- A.2 Hunt processes and Dirichlet forms -- Bibliography -- Index Contents -- 9 A second probabilistic intermezzo -- 3 Bernstein functions -- 8 Thorin–Bernstein functions -- 7 Complete Bernstein functions: properties -- 10 Special Bernstein functions and potentials -- 12 Subordination and Bochner’s functional calculus -- 4 Positive and negative definite functions -- 6 Complete Bernstein functions: representation -- 11 The spectral theorem and operator monotonicity -- Backmatter 13 Potential theory of subordinate killed Brownian motion -- 1 Completely monotone functions -- 15 Examples of complete Bernstein functions -- Frontmatter -- 2 Stieltjes functions -- 14 Applications to generalized diffusions -- 5 A probabilistic intermezzo -- |
| Title | Bernstein Functions |
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| Volume | 37 |
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