5 papers
Schrödinger operators on the half-line with integrable complex potentials
Alexander Pushnitski, František Štampach
In our previous work, we introduced the concept of a \emph{spectral pair} for a half-line Schrödinger operator with a \emph{complex} bounded potential , serving as a substitute…
Sums of projections with random coefficients
Leonid Pastur, Alexander Pushnitski
We study infinite sums \[ {\mathcal P}_{\varkappa}=\sum_{n=-\infty}^\infty \varkappa_n \langle\cdot, ψ_n\rangleψ_n \] of rank-one projections in a Hilbert space, where $\{ψ_n\}_{n\…
Ergodic Hankel operators
Leonid Pastur, Alexander Pushnitski
We introduce a new class of operators: ergodic families of self-adjoint Hankel operators realised as integral operators on the half-line. Inspired by the spectral theory of differe…
The spectral map for weighted Cauchy matrices is an involution
Alexander Pushnitski, Sergei Treil
Let be a natural number. We consider weighted Cauchy matrices of the form \[ \mathcal{C}_{a,A}=\left\{\frac{\sqrt{A_j A_k}}{a_k+a_j}\right\}_{j,k=1}^N, \] where …
The Borg-Marchenko uniqueness theorem for complex potentials
Alexander Pushnitski, František Štampach
We introduce and study a new theoretical concept of \textit{spectral pair} for a Schrödinger operator in with a bounded \textit{complex-valued} potential.…