Knit product of finite groups and sampling

2018/06/28 by García, Antonio G., Hernández-Medina, Miguel A., Ibort, Albert
#20C40 #42C15 #94A20 #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1806.11481

Abstract

A finite sampling theory associated with a unitary representation of a finite non Abelian group G on a Hilbert space is stablished. The non Abelian group G is a knit product N\bowtie H of two finite subgroups N and H. 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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