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## 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

#### Streszczenie

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.

#### Autorzy

• Sameer ChavanIndian Institute of Technology Kanpur
Kanpur 208016, India
e-mail
• V. M. SholapurkarCenter for Postgraduate Studies
in Mathematics
S. P. College
Pune 411030, India
e-mail

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