LEADER 03842nam 2200829Ia 450 001 9910973705003321 005 20250926114550.0 010 $a9786612714696 010 $a9781282714694 010 $a1282714694 010 $a9783110215311 010 $a3110215314 024 7 $a10.1515/9783110215311 035 $a(CKB)2670000000016975 035 $a(EBL)511800 035 $a(PPN)290433339 035 $a(OCoLC)651047685 035 $a(SSID)ssj0000412685 035 $a(PQKBManifestationID)11305559 035 $a(PQKBTitleCode)TC0000412685 035 $a(PQKBWorkID)10368156 035 $a(PQKB)11446990 035 $a(MiAaPQ)EBC511800 035 $a(DE-B1597)36072 035 $a(OCoLC)1002272943 035 $a(OCoLC)1004876469 035 $a(OCoLC)1011470113 035 $a(OCoLC)1013941046 035 $a(OCoLC)979689117 035 $a(OCoLC)987943165 035 $a(OCoLC)992489690 035 $a(OCoLC)999362842 035 $a(DE-B1597)9783110215311 035 $a(Au-PeEL)EBL511800 035 $a(CaPaEBR)ebr10373552 035 $a(CaONFJC)MIL271469 035 $a(Perlego)404075 035 $a(EXLCZ)992670000000016975 100 $a20091012d2010 uy 0 101 0 $aeng 135 $aur||#|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBernstein functions $etheory and applications /$fRene L. Schilling, Renming Song, Zoran Vondracek 205 $a1st ed. 210 $aBerlin $cWalter De Gruyter$dc2010 215 $a1 online resource (327 p.) 225 1 $aDe Gruyter studies in mathematics ;$v37 300 $aDescription based upon print version of record. 311 08$a9783110215304 311 08$a3110215306 320 $aIncludes bibliographical references (p. [291]-308) and index. 327 $tFrontmatter --$tContents --$t1 Completely monotone functions --$t2 Stieltjes functions --$t3 Bernstein functions --$t4 Positive and negative definite functions --$t5 A probabilistic intermezzo --$t6 Complete Bernstein functions: representation --$t7 Complete Bernstein functions: properties --$t8 Thorin-Bernstein functions --$t9 A second probabilistic intermezzo --$t10 Special Bernstein functions and potentials --$t11 The spectral theorem and operator monotonicity --$t12 Subordination and Bochner's functional calculus --$t13 Potential theory of subordinate killed Brownian motion --$t14 Applications to generalized diffusions --$t15 Examples of complete Bernstein functions --$tBackmatter 330 $aThis text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory. An extensive list of complete Bernstein functions with their representations is provided. A self-contained and unified approach to the topic With applications to various fields of mathematics, such as probability theory, potential theory, operator theory, integral equations, functional calculi and complex analysis With an extensive list of complete Bernstein functions. Additional material and corrections can be found on the authors' website. 410 0$aDe Gruyter studies in mathematics ;$v37. 606 $aAnalytic functions 606 $aMonotonic functions 615 0$aAnalytic functions. 615 0$aMonotonic functions. 676 $a515.7 686 $aSK 420$2rvk 700 $aSchilling$b Rene? L$0478394 701 $aSong$b Renming$f1963-$0518274 701 $aVondrac?ek$b Zoran$f1959-$0518275 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910973705003321 996 $aBernstein functions$94438311 997 $aUNINA