2010/08/04 by Currey, by Bradley, Mayeli, Azita
#42C15 #42C40 #43A65 #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1008.0888
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.