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Extensions of positive definite functions on free groups

M. Bakonyi·D. Timotin
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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.

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M. Bakonyi, D. Timotin. 2005-12-01. Extensions of positive definite functions on free groups. https://arxiv.org/abs/math/0512042

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