21 citations · 130 across the 23 of their papers we have counts for
7 papers · 1 filter
Centrally symmetric analytic plane domains are spectrally determined in this class
Hamid Hezari, Steve Zelditch
We prove that, under some generic non-degeneracy assumptions, real analytic, centrally symmetric plane domains are determined by their Dirichlet (resp. Neumann) spectra. We prove t…
Eigenfunction asymptotics and spectral Rigidity of the ellipse
Hamid Hezari, Steve Zelditch
This paper is part of a series concerning the isospectral problem for an ellipse. In this paper, we study Cauchy data of eigenfunctions of the ellipse with Dirichlet or Neumann bou…
The Neumann isospectral problem for trapezoids
Hamid Hezari, Zhiqin Lu, Julie Rowlett
We show that trapezoids with identical Neumann spectra are congruent up to rigid motions of the plane. The proof is based on heat trace invariants and some new wave trace invariant…
A Fulling-Kuchment theorem for the 1D harmonic oscillator
Victor Guillemin, Hamid Hezari
We prove that there exists a pair of "non-isospectral" 1D semiclassical Schrödinger operators whose spectra agree modulo h^\infty. In particular, all their semiclassical trace inva…
Inverse problems in spectral geometry
Kiril Datchev, Hamid Hezari
In this survey we review positive inverse spectral and inverse resonant results for the following kinds of problems: Laplacians on bounded domains, Laplace-Beltrami operators on co…
spectral rigidity of the ellipse
Hamid Hezari, Steve Zelditch
We prove that ellipses are infinitesimally spectrally rigid among domains with the symmetries of the ellipse.