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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On an inclusion of the essential spectrum of Laplacians under non-compact change of metric


Author: Jun Masamune
Journal: Proc. Amer. Math. Soc. 140 (2012), 1045-1052
MSC (2010): Primary 58J50; Secondary 47B25
Published electronically: June 29, 2011
MathSciNet review: 2869089
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Abstract: The stability of essential self-adjointness and an inclusion of the essential spectra of Laplacians under the change of a Riemannian metric on a subset $ K$ of $ M$ are proved. The set $ K$ may have infinite volume measured with the new metric, and its completion may contain a singular set such as the fractal set, to which the metric is not extendable.


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Additional Information

Jun Masamune
Affiliation: Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, Massachusetts 01609-2280
Address at time of publication: Department of Mathematics and Statistics, Pennsylvania State University-Altoona, 3000 Ivyside Park, Altoona, Pennsylvania 16601
Email: jum35@psu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10965-1
PII: S 0002-9939(2011)10965-1
Keywords: Essential self-adjointness, incomplete manifolds, essential spectrum, perturbations
Received by editor(s): March 30, 2010
Received by editor(s) in revised form: September 23, 2010, and December 8, 2010
Published electronically: June 29, 2011
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.