Analysis & PDE 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 $C^{\infty}$ 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