21 citations · 130 across the 23 of their papers we have counts for
5 papers · 1 filter
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…
Lower bounds for volumes of nodal sets: an improvement of a result of Sogge-Zelditch
Hamid Hezari, Zuoqin Wang
We use the Dong-Sogge-Zelditch formula to obtain a lower bound for the volume of the nodal sets of eigenfunctions. Our result improves the recent results of Sogge-Zelditch and in d…
A natural lower bound for the size of nodal sets
Hamid Hezari, Christopher D. Sogge
We prove a natural inequality which implies the known lower bounds for the -dimensional Hausdorff measure of nodal sets for smooth compact manifolds.
Resonant uniqueness of radial semiclassical Schrodinger operators
Kiril Datchev, Hamid Hezari
We prove that radial, monotonic, superexponentially decaying potentials in R^n, n greater than or equal to 1 odd, are determined by the resonances of the associated semiclassical S…