Extensions of positive definite functions on free groups
Functional Analysis
2007-05-23 v1 Operator Algebras
Abstract
An analogue of Krein's extension theorem is proved for operator-valued positive definite functions on free groups. The proof gives also the parametrization of all extensions by means of a generalized type of Szego parameters. One singles out a distinguished completion, called central, which is related to quasi-multiplicative positive definite functions. An application is given to factorization of noncommutative polynomials.
Cite
@article{arxiv.math/0512042,
title = {Extensions of positive definite functions on free groups},
author = {M. Bakonyi and D. Timotin},
journal= {arXiv preprint arXiv:math/0512042},
year = {2007}
}