English

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.

Keywords

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}
}
R2 v1 2026-07-22T17:28:11.366Z