دانلود کتاب Bernstein Functions: Theory and Applications

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Preface to the second edition\nPreface\nIndex of notation\n1 Completely monotone functions\n2 Stieltjes functions\n3 Bernstein functions\n4 Positive and negative definite functions\n5 A probabilistic intermezzo\n6 Complete Bernstein functions\n 6.1 Representation of complete Bernstein functions\n 6.2 Extended complete Bernstein functions\n7 Properties of complete Bernstein functions\n8 Thorin-Bernstein functions\n9 A second probabilistic intermezzo\n10 Transformations of Bernstein functions\n11 Special Bernstein functions and potentials\n 11.1 Special Bernstein functions\n 11.2 Hirsch’s class\n12 The spectral theorem and operator monotonicity\n 12.1 The spectral theorem\n 12.2 Operator monotone functions\n13 Subordination and Bochner’s functional calculus\n 13.1 Semigroups and subordination in the sense of Bochner\n 13.2 A functional calculus for generators of semigroups\n 13.3 Subordination and functional inequalities\n 13.4 Eigenvalue estimates for subordinate processes\n14 Potential theory of subordinate killed Brownian motion\n15 Applications to generalized diffusions\n 15.1 Inverse local time at zero\n 15.2 First passage times\n16 Examples of complete Bernstein functions\n 16.1 Special functions used in the tables\n 16.2 Algebraic functions\n 16.3 Exponential functions\n 16.4 Logarithmic functions\n 16.5 Inverse trigonometric functions\n 16.6 Hyperbolic functions\n 16.7 Inverse hyperbolic functions\n 16.8 Gamma and related special functions\n 16.9 Bessel functions\n 16.10 Miscellaneous functions\n 16.11 CBFs given by exponential representations\n 16.12 Additional comments\nAppendix\n A.1 Vague and weak convergence of measures\n A.2 Hunt processes and Dirichlet forms\nBibliography\nIndex