21 citations · 130 across the 23 of their papers we have counts for
16 papers · 1 filter
Upper bounds on the size of nodal sets for Gevrey and quasianalytic Riemannian manifolds
Hamid Hezari
We find new polynomial upper bounds for the size of nodal sets of eigenfunctions when the Riemannian manifold has a Gevrey or quasianalytic regularity.
The Dirichlet isospectral problem for trapezoids
Hamid Hezari, Zhiqin Lu, Julie Rowlett
We show that non-obtuse trapezoids are uniquely determined by their Dirichlet Laplace spectrum. This extends our previous result, which was only concerned with the Neumann Laplace…
One can hear the shape of ellipses of small eccentricity
Hamid Hezari, Steve Zelditch
We show that if the eccentricity of an ellipse is sufficiently small then up to isometries it is spectrally unique among all smooth domains. We do not assume any symmetry, convexit…
Equidistribution of toral eigenfunctions along hypersurfaces
Hamid Hezari, Gabriel Riviere
We prove a new quantum variance estimate for toral eigenfunctions. As an application, we show that, given any orthonormal basis of toral eigenfunctions and any smooth embedded hype…
Robin spectral rigidity of strictly convex domains with a reflectional symmetry
Hamid Hezari
This is a note on a recent paper of De Simoi-Kaloshin-Wei \cite{DKW}. We show that using their results combined with wave trace invariants of Guillemin-Melrose and the heat trace i…
Quantum ergodicity and norms of restrictions of eigenfunctions
Hamid Hezari
We prove an analogue of Sogge's local estimates for norms of restrictions of eigenfunctions to submanifolds, and use it to show that for quantum ergodic eigenfunctions…