Generalized analogs of the Heisenberg uncertainty inequality
type: Item
instance of: scholarly article
title: Generalized analogs of the Heisenberg uncertainty inequality
zbMATH Open document ID: 1345.22006
author: Ashish Bansal
author: Ajay Kumar
published in: Journal of Inequalities and Applications
publication date: 2016-03-31T00:00:00Z
full work available at URL: https://arxiv.org/abs/1410.3050
review text: Firstly, the authors prove a generalized analog of the Heisenberg uncertainty inequality for \(\mathbb R^n\times K\), where \(K\) is a seperable unimodular locally compact group of type of \(I\). Then they investigate another generalized analog of the Heisenberg uncertainty inequality for the group \(M(n)\), the Euclidean motion group. Lastly, for a class of connected, simply connected nilpotent Lie groups, they prove the Heisenberg uncertainty inequality. Then they give examples of the Heisenberg uncertainty inequality for thread-like nilpotent Lie groups, 2-NPC nilpotent Lie groups, simply connected nilpotent Lie groups and low-dimensional nilpotent Lie groups of dimensions less than or equal to 6.
reviewed by: Öznur Kulak
Mathematics Subject Classification ID: 22E25
Mathematics Subject Classification ID: 43A25
Mathematics Subject Classification ID: 22D10
zbMATH DE Number: 6561531
zbMATH Keywords: Heisenberg uncertainty inequality
zbMATH Keywords: nilpotent Lie group
zbMATH Keywords: Euclidean motion group
zbMATH Keywords: Plancherel formula
zbMATH Keywords: Fourier transform
MaRDI profile type: Publication
OpenAlex ID: W2111211036
Wikidata QID: Q59431450
arXiv ID: 1410.3050
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DOI: 10.1186/S13660-015-0691-7
description: scientific article; zbMATH DE number 6561531