The spectral function of a Riemannian orbifold
type: Item
instance of: scholarly article
title: The spectral function of a Riemannian orbifold
zbMATH Open document ID: 1223.58024
published in: Annals of Global Analysis and Geometry
publication date: 2011-06-03T00:00:00Z
review text: Let \(X\) be a compact orbifold and \(P\) a first-order symmetric elliptic pseudodifferential operator on \(X\) with positive principal symbol. It is known that \(P\) has a discrete spectrum and there exists an orthonormal basis of eigenfunctions \(\{\psi_{j}\}\): \(P\psi_{j}=\mu_{j}\psi_{j}\), where the eigenvalues \(\mu_{j}\) are ordered as \(\mu_{1}\leq\mu_{2}\leq\cdots\). In the paper under review, the authors study the asymptotics of the spectral function \(\sum_{j:\mu_{j}\leq\mu}|\psi_{j}(x_{0})|^{2}\) as \(\mu\) goes to infinity, for a fixed \(x_{0}\in X\). It is noted that the formula depends on \(x_{0}\), in contrast with the case where \(X\) is a (Riemannian) manifold.
reviewed by: Salah Mehdi
Mathematics Subject Classification ID: 58J40
Mathematics Subject Classification ID: 58J37
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 5903717
zbMATH Keywords: spectral function
zbMATH Keywords: orbifold
zbMATH Keywords: wave trace
Wikidata QID: Q115384611
author: Elizabeth Stanhope
author: A. Uribe
MaRDI profile type: Publication
full work available at URL: s10455-010-9244-y
OpenAlex ID: W2012288401
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DOI: 10.1007/S10455-010-9244-Y
description: scientific article; zbMATH DE number 5903717