A. Pushnitski

activity

20202026

most citedThe spectrum of some Hardy kernel matrices

4 citations · 4 across the 10 of their papers we have counts for

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Showing 2025Show all

5 papers · 1 filter

math.SP2025

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\…

math.SP2025

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…

math.RA2025

The spectral map for weighted Cauchy matrices is an involution

Alexander Pushnitski, Sergei Treil

Let $N$ 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 $A_{1}, \dots, A_{N}$ …

math.SP2025

Inverse spectral problems for positive Hankel operators

Alexander Pushnitski, Sergei Treil

A Hankel operator $Γ$ in $L^{2} (R_{+})$ is an integral operator with the integral kernel of the form $h (t + s)$ , where $h$ is known as the kernel function. It is known that $Γ$ …

math.SP2025

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 $H$ in $L^{2} (R_{+})$ with a bounded \textit{complex-valued} potential.…