Extensions of positive definite functions on free groups

Details Extensions of positive definite functions on free groups Extensions of positive definite functions on free groups

2005-12-01

arxiv.org/abs/math/0512042v1

Mathematics

Functional Analysis

Scientific paper

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.

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