Publication: Knit product of finite groups and sampling
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2019-12
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Elsevier
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Abstract
A finite sampling theory associated with a unitary representation of a finite non-abelian group G on a Hilbert space is established. The non-abelian group G is a knit product N⋈H of two finite subgroups N and H where at least N or H is abelian. Sampling formulas where the samples are indexed by either N or H are obtained. Using suitable expressions for the involved samples, the problem is reduced to obtain dual frames in the Hilbert space ℓ2(G) having a unitary invariance property; this is done by using matrix analysis techniques. An example involving dihedral groups illustrates the obtained sampling results.
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Keywords
Dual frames, Finite frames, Finite unitary-invariant subspaces, Knit product of groups, Left-inverses, Sampling expansions, Unitary representation of a group
Bibliographic citation
García, A. G., Hernández-Medina, M. A. & Ibort, A. (2019). Knit Product of Finite Groups and Sampling. Mediterranean Journal of Mathematics, 16(6), 1–16.