Bernstein Functions: Theory and Applications (De Gruyter Studies in Mathematics, 37)

Bernstein functions and the important subclass of complete Bernstein functions appear in various fields of mathematics - often with different definitions and under different names. Probabilists, for example, know Bernstein functions as Laplace exponents, and in harmonic analysis they are called negative definite functions. Complete Bernstein functions are used in complex analysis under the name Pick or Nevanlinna functions, while in matrix analysis and operator theory, the name operator monotone function is more common. When studying the positivity of solutions of Volterra integral equations, various types of kernels appear which are related to Bernstein functions. There exists a considerable amount of literature on each of these classes, but only a handful of texts observe the connections between them or use methods from several mathematical disciplines. This monograph - now in its second revised and extended edition - is about these connections. Compared to the first edition the authors added a substantial amount of new material. Their aim was to retain the overall structure of the text with theoretical material in Chapters 1 to 11 and more specific applications in Chapters 12 to 15.