Bernstein Functions

Many mathematicians may never have heard of Bernstein functions, because in probability they are known as Laplace exponents, in harmonic analysis as negative definite functions, in complex analysis as Pick or Nevanlinna functions, and in matrix analysis and operator theory as monotone function. Schilling (stochastics, Technical U. of Dresden), Renming Song (mathematics, U. of Illinois-Urbana), and Zoran Vondracek (mathematics, U. of Zagreb) examine the features common to all, first introducing the basic classics of functions, then surveying applications of Bernstein and complete Bernstein functions. A final section presents extensive tales of complete Bernstein functions. They have revised and rewritten portions of the 2009 first edition, and added a substantial amount of new material. Annotation c2012 Book News, Inc., Portland, OR (booknews.com)

Rene L. Schilling, Dresden University of Technology, Germany;Renming Song, University of Illinois, Urbana, USA; Zoran Vondra?ek, University of Zagreb, Croatia.