200 citations · 1k across the 51 of their papers we have counts for
56 papers
Stability of spectral partitions with corners
Gregory Berkolaiko, Yaiza Canzani, Graham Cox +2
A spectral minimal partition of a manifold is a decomposition into disjoint open sets that minimizes a spectral energy functional. While it is known that bipartite minimal partitio…
Half-time Range description for the free space wave operator and the spherical means transform
Peter Kuchment, Leonid Kunyansky
The forward problem arising in several hybrid imaging modalities can be modeled by the Cauchy problem for the free space wave equation. Solution to this problems describes propagat…
Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown
Peter Kuchment
The article surveys the known results and conjectures about the analytic properties of dispersion relations and Fermi surfaces for periodic equations of mathematical physics and th…
Spectral shift via "lateral" perturbation
G. Berkolaiko, P. Kuchment
We consider a compact perturbation of a self-adjoint operator with an eigenvalue below its essential spectrum and the corresponding eigenfunctio…
Mikhail Aleksandrovich Shubin. December 19, 1944 -- May 13, 2020
Maxim Braverman, Arnold Dikansky, Leonid Friedlander +8
The article is dedicated to thye memory of a distinguished mathematician Professor Misha Shubin
Dispersion relations and spectra of periodically perforated structures
Peter Kuchment, Jari Taskinen
We establish absolute continuity of the spectrum of a periodic Schrödiner operator in R^n with periodic perforations. We also prove analytic dependece of the dispersion relation on…