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Sampling in unitary invariant subspaces associated to LCA groups

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2017-12
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Springer
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Abstract
In this paper a sampling theory for unitary invariant subspaces associated to locally compact abelian (LCA) groups is deduced. Working in the LCA group context allows to obtain, in a unified way, sampling results valid for a wide range of problems which are interesting in practice, avoiding also cumbersome notation. Along with LCA groups theory, the involved mathematical technique is that of frame theory which meets matrix analysis when appropriate dual frames are computed.
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LCA groups, Unitary representation of a LCA group, Unitary-invariant subspaces, Frames, Dual frames, Sampling expansions
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García, A.G., Hernández-Medina, M.A. & Pérez-Villalón, G. (2017). Sampling in Unitary Invariant Subspaces Associated to LCA Groups. Results in Mathematics, vol. 72, pp. 1725–1745.