A frequency space for the Heisenberg group

The Frequency Space of a Free Group

We analyze the structure of the frequency space Q(F ) of a nonabelian free group F = F (a1, . . . , ak) consisting of all shift-invariant Borel probability measures on ∂F and construct a natural action of Out(F ) on Q(F ). In particular we prove that for any outer automorphism φ of F the conjugacy distortion spectrum of φ, consisting of all numbers ||φ(w)||/||w||, where w is a nontrivial conjug...

Issues in Deconvolution, from Euclidean Space to the Heisenberg Group

We review some of the important results on deconvolution, particularly the multichannel deconvolution problem, for the setting of Euclidean space, focusing on the central role of the Hörmander strongly coprime condition in this area of analysis. We then address the problem of deconvolution in the Heisenberg group setting, beginning with the results of [16]. We also extend the results of [16] to...

A Necessary Condition for Weyl-Heisenberg Frames

A Non-perturbative Real-space Renormalization Group Scheme for the Spin- Xxx Heisenberg Model

In this article we apply a recently invented analytical real-space renormalization group formulation which is based on numerical concepts of the density matrix renormalization group. Within a rigorous mathematical framework we construct non-perturbative renormalization group transformations for the spin1 2 XXX Heisenberg model in the finite temperature regime. The developed renormalization grou...

Sampling theorems for the Heisenberg group

In the first part of the paper a general notion of sampling expansions for locally compact groups is introduced, and its close relationship to the discretisation problem for generalised wavelet transforms is established. In the second part, attention is focussed on the simply connected nilpotent Heisenberg group H. We derive criteria for the existence of discretisations and sampling expansions ...