Abstract Let Y={f (i), Af (i),…, A lif (i): i∈ Ω}, where A is a bounded operator on ℓ 2 (I). The
problem under consideration is to find necessary and sufficient conditions on A, Ω,{li: i∈ Ω} …

In this chapter, we review some of the recent developments and prove new results
concerning frames and Bessel systems generated by iterations of the form A ng: g∈ G, n= 0 …

Given a simply connected nilpotent Lie group having unitary irreducible representations that
are square-integrable modulo the center, we use operator-valued periodization to give a …

In this article, we establish theory of semi-orthogonal Parseval wavelets associated with
generalized multiresolution analysis (GMRA) for local fields of positive characteristics …

We consider left invariant multiplicity free subspaces of L² (N) where N is the Heisenberg
group. We prove a necessary and sufficient density condition in order that such subspaces …

It is the main goal of this text to study certain aspects of time-frequency analysis on the 2n1-
dimensional Heisenberg group. More specifically, we will discuss how the well-studied …

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. For a …

Let G be a locally compact abelian (LCA) group equipped with a Haar measure. A collection
of measurable subsets {Ω _i\} _ i= 1^ m Ω ii= 1 m in ̂ GG^ is called a Riesz wavelet …

In this paper, we attempt to obtain sufficient conditions for the existence of tight wavelet
frame sets in locally compact abelian groups. The condition is generated by modulating a …

We prove and construct Shannon-like Parseval wavelet frames for a class of two step
connected, and simply connected nilpotent Lie groups, using a mixture of representation …