On Discrete Groups of Euclidean Isometries: Representation Theory, Harmonic Analysis and Splitting Properties.

We study structural properties and the harmonic analysis of discrete subgroups of the Euclidean group. In particular, we 1. obtain an efficient description of their dual space, 2. develop Fourier analysis methods for periodic mappings on them, and 3. prove a Schur-Zassenhaus type splitting result. [ABSTRACT FROM AUTHOR]