Sergey Naboko

Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDES and block operator matrices

Starting with an adjoint pair of operators, under suitable abstract versions of standard PDE hypotheses, we consider the Weyl M-function of extensions of the operators. The extensions are determined by abstract boundary conditions and we establish results on the relationship between the M-function as an analytic function of a spectral parameter and the spectrum of the extension. We also give an example where the M-function does not contain the whole spectral information of the resolvent, and show that the results can be applied to elliptic PDEs where the M-function corresponds to the Dirichlet to Neumann map.

On the absolutely continuous spectrum in a model of an irreversible quantum graph

A family

Simplicity of eigenvalues in Anderson-type models

\mathbf{A}_\alpha

Spectral Theory and Analysis : Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2008, Bedlewo, Poland

of differential operators depending on a real parameter

The finite section method for dissipative operators

\alpha \ge 0

FRACTIONAL MOMENT METHODS FOR ANDERSON LOCALIZATION IN THE CONTINUUM

is considered. This family was suggested by Smilansky as a model of an irreversible quantum system. We find the absolutely continuous spectrum

Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach

\sigma_{a.c.}

Green Matrix Estimates of Block Jacobi Matrices I: Unbounded Gap in the Essential Spectrum

of the operator

On the Instability of the Essential Spectrum for Block Jacobi Matrices

\mathbf{A}_\alpha

On New Relations Between Spectral Properties of Jacobi Matrices and Their Coefficients

and its multiplicity for all values of the parameter. The spectrum of