Primitive tilings and coherent frames
type: Item
instance of: scholarly article
title: Primitive tilings and coherent frames
zbMATH Open document ID: 1478.42033
author: Luis S. Silvestre
author: Eden P. Miro
author: Job A. Nable
published in: Journal of Geometry and Symmetry in Physics
publication date: 2021-09-08T00:00:00Z
review text: Coherent states was first introduced by Schrödinger in the context of the quantum harmonic oscillators, in his investigation of classical to quantum transition. Coherent states brought about the area of study focused on coherent frames. These are sequences of the form \(\{\pi(\lambda) f\}_{\lambda \in \Lambda}\) in a Hilbert space \(\mathcal{H}\) based on a representation \(\pi\) of a group \(G\) acting on \(\mathcal{H}\), some window function \(f \in \mathcal{H}\), and a discrete subset \(\Lambda \subset G\), for which there exist constants \(A, B>0\) such that \[ A\|h\|^{2} \leq \sum_{\lambda \in \Lambda}|\langle h, \pi(\lambda) f\rangle|^{2} \leq B\|h\|^{2} \quad \text { for all } \quad h \in \mathcal{H}. \] Coherent frames are mostly characterized by conditions on the generating discrete subset. For instance, the Balian-Low theorem describes Gabor frames based on periodic lattices and provides a density condition on lattices. The objective of this paper is to characterize primitive tilings of Lie groups generating aperiodic coherent frames.
reviewed by: Pierluigi Vellucci
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 46B15
Mathematics Subject Classification ID: 52C23
zbMATH DE Number: 7392461
zbMATH Keywords: coherent frame
zbMATH Keywords: primitive tiling
zbMATH Keywords: primitive substitution tiling system
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7392461