Completely monotone functions of finite order and Agler's conditions
Tom 226 / 2015
Studia Mathematica 226 (2015), 229-258 MSC: Primary 47A13, 43A35; Secondary 44A10, 47B20. DOI: 10.4064/sm226-3-3
Motivated by some structural properties of Drury–Arveson $d$-shift, we investigate a class of functions consisting of polynomials and completely monotone functions defined on the semi-group $\mathbb N$ of non-negative integers, and its operator-theoretic counterpart which we refer to as the class of completely hypercontractive tuples of finite order. We obtain a Lévy–Khinchin type integral representation for the spherical generating tuples associated with such operator tuples and discuss its applications.