21 citations · 130 across the 23 of their papers we have counts for
5 papers · 1 filter
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…
Inner radius of nodal domains of quantum ergodic eigenfunctions
Hamid Hezari
In this short note we show that the lower bounds of Mangoubi on the inner radius of nodal domains can be improved for quantum ergodic sequences of eigenfunctions, according to a ce…
Applications of small scale quantum ergodicity in nodal sets
Hamid Hezari
The goal of this article is to draw new applications of small scale quantum ergodicity in nodal sets of eigenfunctions. We show that if quantum ergodicity holds on balls of shrinki…
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…