Sampling Associated with a Unitary Representation of a Semi-Direct Product of Groups: A Filter Bank Approach

This article belongs to the Special Issue New trends on Symmetry and Topology in Quantum Mechanics ; An abstract sampling theory associated with a unitary representation of a countable discrete non abelian group G, which is a semi-direct product of groups, on a separable Hilbert space is studied. A suitable expression of the data samples, the use of a filter bank formalism and the corresponding frame analysis allow for fixing the mathematical problem to be solved: the search of appropriate dual frames for l2(G). An example involving crystallographic groups illustrates the obtained results by using either average or pointwise samples. ; This research was funded by the grant MTM2017-84098-P from the Spanish Ministerio de Economía y Competitividad (MINECO).