Harmonic Analysis and Degenerate Diffusions on Euclidean Groups

We take up an idea, introduced by Chirikjian andKyatkin, of analyzing a family of left-invariant diffusion equations on Euclidean groups via the group Fourier transform. These diffusion equations model the probability distribution of the orientation in space of certain polymers in solution, including DNA. We study the evolution equations satisfied by the Fourier coefficients of such a solution. Our main task here is to estimate these Fourier coefficients sufficiently well that one canestimate the error in truncating the group inverse Fourier transform to afinite region.