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100   $a20120305d2012      uy             0
101 0 $aeng
135   $aurnn#---|u||u
181   $ctxt
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183   $acr
200 10$aBernstein functions$b[electronic resource] $etheory and applications /$fby Rene L. Schilling, Renming Song, Zoran Vondracek
205   $a2nd ed.
210   $aBerlin $cDe Gruyter$dc2012
215   $a1 online resource (424 p.)
225 0 $aDe Gruyter Studies in Mathematics ;$v37
300   $aDescription based upon print version of record.
311 0 $a3-11-026933-3 
311 0 $a3-11-025229-5 
320   $aIncludes bibliographical references (p. [383]-) and index.
327   $tFront matter --$tPreface to the second edition --$tPreface --$tContents --$tIndex of notation --$tChapter 1. Laplace transforms and completely monotone functions --$tChapter 2. Stieltjes functions --$tChapter 3. Bernstein functions --$tChapter 4. Positive and negative definite functions --$tChapter 5. A probabilistic intermezzo --$tChapter 6. Complete Bernstein functions --$tChapter 7. Properties of complete Bernstein functions --$tChapter 8. Thorin-Bernstein functions --$tChapter 9. A second probabilistic intermezzo --$tChapter 10. Transformations of Bernstein functions --$tChapter 11. Special Bernstein functions and potentials --$tChapter 12. The spectral theorem and operator monotonicity --$tChapter 13. Subordination and Bochner's functional calculus --$tChapter 14. Potential theory of subordinate killed Brownian motion --$tChapter 15. Applications to generalized diffusions --$tChapter 16. Examples of complete Bernstein functions --$tAppendix --$tBibliography --$tIndex
330   $aBernstein functions appear in various fields of mathematics, e.g. probability theory, potential theory, operator theory, functional analysis and complex analysis - often with different definitions and under different names. Among the synonyms are `Laplace exponent' instead of Bernstein function, and complete Bernstein functions are sometimes called `Pick functions', `Nevanlinna functions' or `operator monotone functions'. This monograph - now in its second revised and extended edition - offers a self-contained and unified approach to Bernstein functions and closely related function classes, bringing together old and establishing new connections. For the second edition the authors added a substantial amount of new material. As in the first edition Chapters 1 to 11 contain general material which should be accessible to non-specialists, while the later Chapters 12 to 15 are devoted to more specialized topics. An extensive list of complete Bernstein functions with their representations is provided.
410  3$aDe Gruyter Studies in Mathematics
606   $aAnalytic functions
606   $aMonotonic functions
606   $aQuasianalytic functions
610   $aBernstein Function.
610   $aMonotone Function.
610   $aProbability Measure.
610   $aSemigroup.
610   $aTheory.
615  0$aAnalytic functions.
615  0$aMonotonic functions.
615  0$aQuasianalytic functions.
676   $a515/.8
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   $a9910786435503321
996   $aBernstein functions$93749655
997   $aUNINA