A noncommutative half-angle formula

Publisher: Cambridge University Press

E-ISSN: 1755-1633|69|3|369-382

ISSN: 0004-9727

Source: Bulletin of the Australian Mathematical Society, Vol.69, Iss.3, 2004-06, pp. : 369-382

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Abstract

The half-angle formulæ, familiar from trigonometry, can be used to compute the polar decomposition of the operator on l2() 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.