February Fourier Talks 2007

Degenerate Diffusions on Motion Groups: An Application of Noncommutative Harmonic Analysis

Degenerate diffusion equations on the Euclidean motion groups arise in a number of different fields including Robotics, Polymer Statistical Mechanics, and Optical Communications. This talk reviews several of these application areas and describes how the Fourier transform of functions on motion groups can be used to solve these equations. In particular, operational properties, the convolution theorem, and Fourier reconstruction formula based on truncated infinite-dimensional irreducible unitary representations for these groups are used.