20 citations · 47 across the 23 of their papers we have counts for
6 papers · 1 filter
On negative eigenvalues of two-dimensional Schroedinger operators with singular potentials
Martin Karuhanga, Eugene Shargorodsky
We present upper estimates for the number of negative eigenvalues of two-dimensional Schroedinger operators with potentials generated by Ahlfors regular measures of arbitrary dimen…
Level sets of the resolvent norm of a linear operator revisited
E. B. Davies, Eugene Shargorodsky
It is proved that the resolvent norm of an operator with a compact resolvent on a Banach space cannot be constant on an open set if the underlying space or its dual is complex…
On the limit behaviour of second order relative spectra of self-adjoint operators
Eugene Shargorodsky
It is well known that the standard projection methods allow one to recover the whole spectrum of a bounded self-adjoint operator but they often lead to spectral pollution, i.e. to…
On negative eigenvalues of two-dimensional Schrödinger operators
Eugene Shargorodsky
The paper presents estimates for the number of negative eigenvalues of a two-dimensional Schrödinger operator in terms of type Orlicz norms of the potential and proves a…
Spectral pollution and second order relative spectra for self-adjoint operators
Michael Levitin, Eugene Shargorodsky
We consider the phenomenon of spectral pollution arising in calculation of spectra of self-adjoint operators by projection methods. We suggest a strategy of dealing with spectral p…
Quasi-conformal mappings and periodic spectral problems in dimension two
E. Shargorodsky, A. V. Sobolev
We study spectral properties of second order elliptic operators with periodic coefficients in dimension two. These operators act in periodic simply-connected waveguides, with eithe…