Publication: Sampling Associated with a Unitary Representation of a Semi-Direct Product of Groups: A Filter Bank Approach
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2019-04-12
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MDPI
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Abstract
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.
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This article belongs to the Special Issue New trends on Symmetry and Topology in Quantum Mechanics
Keywords
Semi-direct product of groups, Unitary representation of a group, Lca groups, Dual frames, Sampling expansions
Bibliographic citation
García, A. G., Hernández-Medina, M. A. y Pérez-Villalón, G. (2019). Sampling Associated with a Unitary Representation of a Semi-Direct Product of Groups: A Filter Bank Approach. Symmetry, 11(4), 529.