Bernstein Functions: Theory and Applications
Bernstein 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.
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11 Special Bernstein functions and potentials
12 The spectral theorem and operator monotonicity
13 Subordination and Bochners functional calculus
14 Potential theory of subordinate killed Brownian motion
15 Applications to generalized diffusions
16 Examples of complete Bernstein functions