The Bloch Transform on Lp-Spaces

We investigate the Bloch Transform on Bochner Lebesgue Spaces. A decomposition in terms of vector valued Fourier Series leads to the study of translation invariant operators on sequence spaces. These operators act like multiplication operators. We proof multiplier theorems for the Bloch Transform, which are used to derive the band gap structure of the spectrum for general periodic operators. The results are applied to partial differential operators.