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Completely monotone functions of finite order and Agler's conditions

Volume 226 / 2015

Sameer Chavan, V. M. Sholapurkar 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.


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

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