Lie Groups III: Integration, Convolution, and Fourier Analysis

Abstract

Functions on Lie groups can be integrated almost as easily as functions on Rn. In many applications, a special kind of Lie group arises. This is the unimodular Lie group. The integral of functions on unimodular Lie groups has the nice property that it is invariant under shifts of the argument of the function, both from the left and the right. The integral on a Lie group can be decomposed into integrals over a subgroup and a coset space.