The half-angle formulæ, familiar from trigonometry, can be used to compute the polar decomposition of the operator on l²(ℤ) 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.
Relation
Bulletin of the Australian Mathematical Society Vol. 69, p. 369-382