04154nam 2200721Ia 450 991046298030332120211030005047.03-11-026900-71-283-85675-110.1515/9783110269338(CKB)2670000000309314(EBL)893312(OCoLC)820121236(SSID)ssj0000991253(PQKBManifestationID)11576893(PQKBTitleCode)TC0000991253(PQKBWorkID)10988954(PQKB)10346973(MiAaPQ)EBC893312(DE-B1597)173792(OCoLC)979912211(DE-B1597)9783110269338(PPN)175488177(Au-PeEL)EBL893312(CaPaEBR)ebr10634604(CaONFJC)MIL416925(EXLCZ)99267000000030931420120305d2012 uy 0engurnn#---|u||utxtccrBernstein functions[electronic resource] theory and applications /by Rene L. Schilling, Renming Song, Zoran Vondracek2nd ed.Berlin De Gruyterc20121 online resource (424 p.)De Gruyter Studies in Mathematics ;37Description based upon print version of record.3-11-026933-3 3-11-025229-5 Includes bibliographical references (p. [383]-) and index.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 --IndexBernstein 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.De Gruyter Studies in MathematicsAnalytic functionsMonotonic functionsQuasianalytic functionsElectronic books.Analytic functions.Monotonic functions.Quasianalytic functions.515/.8Schilling René L478394Song Renming1963-518274Vondraček Zoran1959-518275MiAaPQMiAaPQMiAaPQBOOK9910462980303321Bernstein functions2441406UNINA