The density theorem for discrete series representations restricted to lattices
José Luis Romero (University of Vienna, Austrian Academy of Sciences)
J.T. van Velthoven (TU Delft - Analysis)
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Abstract
This article considers the relation between the spanning properties of lattice orbits of discrete series representations and the associated lattice co-volume. The focus is on the density theorem, which provides a trichotomy characterizing the existence of cyclic vectors and separating vectors, and frames and Riesz sequences. We provide an elementary exposition of the density theorem, that is based solely on basic tools from harmonic analysis, representation theory, and frame theory, and put the results into context by means of examples.
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