Harmonic analysis on tori
type: Item
instance of: scholarly article
title: Harmonic analysis on tori
zbMATH Open document ID: 0629.42013
DOI: 10.1007/BF00046583
author: Steen Pedersen
author: Palle Jorgensen
published in: Acta Applicandae Mathematicae
publication date: 1987-01-01T00:00:00Z
review text: The authors consider a measurable subset \(\Omega \subseteq {\mathbb{R}}^ n\) with spectral set \(\Lambda\). It is not assumed that \(\Lambda\) is a lattice. Instead it is assumed that \(\Lambda\) is the union of shifts of the dual of a lattice. Under these circumstances, necessary and sufficient conditions are derived for \(\Omega\) to be the fundamental domain of some lattice in \({\mathbb{R}}^ n\). A variety of applications are supplied.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 42A65
Mathematics Subject Classification ID: 20C99
Mathematics Subject Classification ID: 47L60
Mathematics Subject Classification ID: 47L30
zbMATH DE Number: 4023961
zbMATH Keywords: dual lattice
zbMATH Keywords: joint spectrum
zbMATH Keywords: induced representations
zbMATH Keywords: projection
zbMATH Keywords: fundamental domain
zbMATH Keywords: applications
reviewed by: Steven G. Krantz
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00046583
OpenAlex ID: W2000585002
description: scientific article; zbMATH DE number 4023961