7 papers
Eigenfunctions of positive integral Hankel operators
Alexander Pushnitski
We consider bounded positive semi-definite Hankel operators , realised as integral operators on the positive semi-axis. For each value of , not necessarily in the spectrum of…
Inverse spectral problems for positive Hankel operators
Alexander Pushnitski, Sergei Treil
A Hankel operator in is an integral operator with the integral kernel of the form , where is known as the kernel function. It is known that $Î…
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 \[ {\mathcal P}_{\varkappa}=\sum_{n=-\infty}^\infty \varkappa_n \langle\cdot, Ï_n\rangleÏ_n \] of rank-one projections in a Hilbert space, where $\{Ï_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 …