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We study structural properties and the harmonic analysis of discretesubgroups of the Euclidean group. In particular, we 1. obtain an efficientdescription of their dual space, 2. develop Fourier analysis methods forperiodic mappings on them, and 3. prove a Schur-Zassenhaus type splittingresult.

On discrete groups of Euclidean isometries: representation theory, harmonic analysis and splitting properties