Spectral theory for Borel sets in \(\mathbb{R}{}^ n\) of finite measure
type: Item
instance of: scholarly article
title: Spectral theory for Borel sets in \(\mathbb{R}{}^ n\) of finite measure
zbMATH Open document ID: 0774.42021
DOI: 10.1016/0022-1236(92)90101-N
author: Steen Pedersen
author: Palle Jorgensen
published in: Journal of Functional Analysis
publication date: 1993-01-16T00:00:00Z
review text: A pair \((\Omega,\Lambda)\) with \(\Omega\) and \(\Lambda\) subsets of \({\mathbf R}^ n\) with \(\Omega\) of finite measure is called a spectral pair if the functions \(e^{\lambda\cdot x}\) are an orthonormal basis for \(L^ 2(\Omega)\). It is shown that any spectral pair may be factored in the Cartesian product of a fundamental domain with its dual lattice and a so-called simple factor. Simple factors can be described by certain finite coverings of an associated torus and relations of generated \(C^*\)- algebras.
Mathematics Subject Classification ID: 42C30
zbMATH DE Number: 90037
zbMATH Keywords: Borel sets of finite measure
zbMATH Keywords: orthonormal basis
zbMATH Keywords: spectral pair
zbMATH Keywords: simple factor
MaRDI profile type: Publication
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full work available at URL: 0022-1236(92)90101-n
OpenAlex ID: W2066340142
description: scientific article; zbMATH DE number 90037