03842nam 2200829Ia 450 991097370500332120250926114550.09786612714696978128271469412827146949783110215311311021531410.1515/9783110215311(CKB)2670000000016975(EBL)511800(PPN)290433339(OCoLC)651047685(SSID)ssj0000412685(PQKBManifestationID)11305559(PQKBTitleCode)TC0000412685(PQKBWorkID)10368156(PQKB)11446990(MiAaPQ)EBC511800(DE-B1597)36072(OCoLC)1002272943(OCoLC)1004876469(OCoLC)1011470113(OCoLC)1013941046(OCoLC)979689117(OCoLC)987943165(OCoLC)992489690(OCoLC)999362842(DE-B1597)9783110215311(Au-PeEL)EBL511800(CaPaEBR)ebr10373552(CaONFJC)MIL271469(Perlego)404075(EXLCZ)99267000000001697520091012d2010 uy 0engur||#||||||||txtccrBernstein functions theory and applications /Rene L. Schilling, Renming Song, Zoran Vondracek1st ed.Berlin Walter De Gruyterc20101 online resource (327 p.)De Gruyter studies in mathematics ;37Description based upon print version of record.9783110215304 3110215306 Includes bibliographical references (p. [291]-308) and index.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 --BackmatterThis 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.De Gruyter studies in mathematics ;37.Analytic functionsMonotonic functionsAnalytic functions.Monotonic functions.515.7SK 420rvkSchilling René L478394Song Renming1963-518274Vondraček Zoran1959-518275MiAaPQMiAaPQMiAaPQBOOK9910973705003321Bernstein functions4438311UNINA