Bulletin of the Australian Mathematical Society

Research Article

A noncommutative half-angle formula

George Willisa1

a1 Department of Mathematics, University of Newcastle, Callaghan NSW 2308, Australia, e-mail: george@math.newcastle.edu.au

The half-angle formulæ, familiar from trigonometry, can be used to compute the polar decomposition of the operator on l2(xs2124) of convolution by δ0 + δ1. This calculation is extended here to a non-commutative setting by computing the polar decomposition of certain convolution operators on the spaces of square integrable functions of free groups.

(Received January 22 2003)