Vol. 5, No. 5, 2012
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$C^{\infty} $ spectral rigidity of the ellipse

Hamid Hezari and Steve Zelditch
Vol. 5 (2012), No. 5, 1105–1132
DOI: 10.2140/apde.2012.5.1105
Abstract

We prove that ellipses are infinitesimally spectrally rigid among C∞ domains with the symmetries of the ellipse.

Keywords
inverse spectral problems, spectral rigidity, isospectral deformations, ellipses
Mathematical Subject Classification 2010
Primary: 35PXX
Milestones
Received: 4 May 2011
Revised: 11 July 2012
Accepted: 6 August 2012
Published: 29 December 2012
Authors
Hamid Hezari
Department of Mathematics
University of California
Irvine, CA 92697
United States
Steve Zelditch
Department of Mathematics
Northwestern University
2033 Sheridan Road
Evanston, IL 60208-2370
United States