JournalsjstVol. 12, No. 1pp. 23–52

Eigenfunction asymptotics and spectral rigidity of the ellipse

  • Hamid Hezari

    University of California, Irvine, USA
  • Steve Zelditch

    Northwestern University, Evanston, USA
Eigenfunction asymptotics and spectral rigidity of the ellipse cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

Microlocal defect measures for Cauchy data of Dirichlet, resp. Neumann, eigenfunctions of an ellipse EE are determined. We prove that, for any invariant curve for the billiard map on the boundary phase space BEB^* E of an ellipse, there exists a sequence of eigenfunctions whose Cauchy data concentrates on the invariant curve. We use this result to give a new proof that ellipses are infinitesimally spectrally rigid among CC^\infty domains with the symmetries of the ellipse.

Cite this article

Hamid Hezari, Steve Zelditch, Eigenfunction asymptotics and spectral rigidity of the ellipse. J. Spectr. Theory 12 (2022), no. 1, pp. 23–52

DOI 10.4171/JST/393