2 Stieltjes functions

Kapitel in diesem Buch

1. Frontmatter i
2. Contents v
3. 1 Completely monotone functions 1
4. 2 Stieltjes functions 11
5. 3 Bernstein functions 15
6. 4 Positive and negative definite functions 25
7. 5 A probabilistic intermezzo 34
8. 6 Complete Bernstein functions: representation 49
9. 7 Complete Bernstein functions: properties 62
10. 8 Thorin–Bernstein functions 73
11. 9 A second probabilistic intermezzo 80
12. 10 Special Bernstein functions and potentials 92
13. 11 The spectral theorem and operator monotonicity 110
14. 12 Subordination and Bochner’s functional calculus 130
15. 13 Potential theory of subordinate killed Brownian motion 174
16. 14 Applications to generalized diffusions 185
17. 15 Examples of complete Bernstein functions 214
18. Backmatter 281