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arXiv · 1804.04974

Semi-direct product of groups, filter banks and sampling

Antonio G. García·Miguel A. Hernández-Medina·Gerardo Pérez-Villalón
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Abstract

An abstract sampling theory associated to 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 and the use of a filter bank formalism allows to fix the mathematical problem to be solved: the search of appropriate dual frames for $\ell^2(G)$. An example involving crystallographic groups illustrates the obtained results by using average or pointwise samples.

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Antonio G. García, Miguel A. Hernández-Medina, Gerardo Pérez-Villalón. 2018-04-13. Semi-direct product of groups, filter banks and sampling. https://arxiv.org/abs/1804.04974

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