On an inclusion of the essential spectrum of Laplacians under non-compact change of metric
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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.References
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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
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 1045-1052
- MSC (2010): Primary 58J50; Secondary 47B25
- DOI: https://doi.org/10.1090/S0002-9939-2011-10965-1
- MathSciNet review: 2869089