Derivatives of the spectral function and Sobolev norms of eigenfunctions on a closed Riemannian manifold
type: Item
instance of: scholarly article
title: Derivatives of the spectral function and Sobolev norms of eigenfunctions on a closed Riemannian manifold
zbMATH Open document ID: 1083.35072
DOI: 10.1023/B:AGAG.0000042902.46202.69
author: Bin Xu
published in: Annals of Global Analysis and Geometry
publication date: 2004-11-22T00:00:00Z
review text: The paper deals with the spectral function and with the unit spectral projection operator, with respect to the Laplace-Beltrami operator on a closed Riemannian manifold. It generalizes the result of Hörmander on the one-term asymptotic expansion of the spectral function to derivatives of the spectral function. Moreover, it extends sharp estimates of the spectral projection operator. Some applications to spherical harmonics are presented.
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 2117699
zbMATH Keywords: Laplace-Beltrami operator
zbMATH Keywords: spectral function
zbMATH Keywords: spectral projection operator
zbMATH Keywords: Sobolev norms of eigenfunctions
Wikidata QID: Q115335116
reviewed by: Pavel Burda
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2117699