2010/08/04 by by Bradley Currey, Currey, by Bradley, Azita Mayeli +1
Mathematics · #42C15 #42C40 #43A65 #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT) #math.FA #math.RT #msc:42C15 #msc:42C40 #msc:43A65
paper · pdf · doi:10.48550/arxiv.1008.0888
Keywords and phrases: frame, dilation, wavelet, Baumslag-Solitar group, shearlet
arxiv created 2010/08/04 · arxiv updated 2010/08/06
In this work we introduce a class of discrete groups containing subgroups of abstract translations and dilations, respectively. A variety of wavelet systems can appear as π(\G)ψ, where π is a unitary representation of a wavelet group and \G is the abstract pseudo-lattice \G. We prove a condition in order that a Parseval frame π(\G)ψ can be dilated to an orthonormal basis of the form τ(\G)Ψ where τ is a super-representation of π. For a subclass of groups that includes the case where the translation subgroup is Heisenberg, we show that this condition always holds, and we cite familiar examples as applications.