03934nam 2200817Ia 450 991079233400332120230725023336.01-282-71469-497866127146963-11-021531-410.1515/9783110215311(CKB)2670000000016975(EBL)511800(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(EXLCZ)99267000000001697520091012d2010 uy 0engur|||||||||||txtccrBernstein functions[electronic resource] theory and applications /René L. Schilling, Renming Song, Zoran VondračekBerlin Walter De Gruyterc20101 online resource (327 p.)De Gruyter studies in mathematics ;37Description based upon print version of record.3-11-021530-6 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 functionsBernstein Functions.Complete Bernstein Functions.Completely Monotone Function.Laplace Transform.Stieltjes Function/Transform.Analytic functions.Monotonic functions.515.7SK 420rvkSchilling René L478394Song Renming1963-518274Vondraček Zoran1959-518275MiAaPQMiAaPQMiAaPQBOOK9910792334003321Bernstein functions3749655UNINA