Generalized uncertainty principles on spaces of homogeneous type
type: Item
instance of: scholarly article
title: Generalized uncertainty principles on spaces of homogeneous type
zbMATH Open document ID: 0834.43008
author: Andrea R. Nahmod
published in: Journal of Functional Analysis
publication date: 1994-07-04T00:00:00Z
review text: The author presents a generalized version of Weyl's law and the Heisenberg uncertainty principle on connected spaces of homogeneous type with finite volume (e.g. Riemannian manifolds or fractals as well). Theorems proved in this interesting paper establish a correspondence between the geometry and spectral properties of some model positive operator \(D_\varepsilon\), a substitute for \((- \Delta)^{\varepsilon/2}\) on compact manifolds, and the geometry of its underlying space. Here \(\varepsilon\) is a sufficiently small positive number.
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35P20
zbMATH DE Number: 599828
zbMATH Keywords: differential operator
zbMATH Keywords: wavelet analysis
zbMATH Keywords: \(\gamma\)-lattices
zbMATH Keywords: Weyl's law
zbMATH Keywords: Heisenberg uncertainty principle
zbMATH Keywords: spaces of homogeneous type
reviewed by: Elena Trofimchuk
MaRDI profile type: Publication
full work available at URL: jfan.1994.1007
OpenAlex ID: W2005100575
DOI: 10.1006/JFAN.1994.1007
description: scientific article; zbMATH DE number 599828