Extension of positive definite functions and Connes' embedding conjecture

TL;DR

This paper proposes a strengthened conjecture related to positive definite functions on free groups and demonstrates that its validity would imply Connes' embedding conjecture, linking harmonic analysis with operator algebra conjectures.

Contribution

It formulates a new conjecture extending positive definite functions and shows its implication for Connes' embedding conjecture, advancing understanding in operator algebras.

Findings

Conjecture links positive definite functions to Connes' embedding.

Proving the conjecture would imply Connes' embedding conjecture.

Provides a new perspective connecting harmonic analysis and operator algebras.

Abstract

In this paper we formulate a conjecture which is a strengthening of an extension theorem of Bakonyi and Timotin for positive definite functions on the free group on two generators. We prove that this conjecture implies Connes' embedding conjecture.