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Bernstein functions; theory and applications.


Bernstein functions; theory and applications.

Schilling, Rene L. et al.

De Gruyter


313 pages



de Gruyter studies in mathematics; 37


Many mathematicians may not have heard of Berstein functions, because in many branches of the field, they are called different names: Laplace exponents, negative definite functions, Pick or Nevanlinna functions, operator monotone functions, and so on. Mathematicians Schilling (Technical U. Dresden), Zoran Vondracek (U. of Zagreb) and Renming Song (U. of Illinois-Urbana-Champaign) explain the features and methods that are common across the varieties at a level appropriate to researchers and graduate students. Their topics include completely monotone functions, positive and negative definite functions, representation and properties of complete Bernstein functions, the spectral theorem and operator monotonicity, a potential theory of subordinate killed Brownian motion, and applications to generalized diffusions.

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Publication:SciTech Book News
Article Type:Book review
Date:Jun 1, 2010
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