200 citations · 1k across the 51 of their papers we have counts for
4 papers · 1 filter
On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators
Peter Kuchment, Boris Vainberg
The article is devoted to the following question. Consider a periodic self-adjoint difference (differential) operator on a graph (quantum graph) G with a co-compact free action of…
A range description for the planar circular Radon transform
Gaik Ambartsoumian, Peter Kuchment
The transform considered in the paper integrates a function supported in the unit disk on the plane over all circles centered at the boundary of this disk. Such circular Radon tran…
Coincidence of length spectra does not imply isospectrality
S. A. Fulling, Peter Kuchment
Penrose--Lifshits mushrooms are planar domains coming in nonisometric pairs with the same geodesic length spectrum. Recently S. Zelditch raised the question whether such billiards…
Liouville theorems and spectral edge behavior on abelian coverings of compact manifolds
Peter Kuchment, Yehuda Pinchover
The paper describes relations between Liouville type theorems for solutions of a periodic elliptic equation (or a system) on an abelian cover of a compact Riemannian manifold and t…