A. Pushnitski

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math.SP2026

Eigenfunctions of positive integral Hankel operators

Alexander Pushnitski

We consider bounded positive semi-definite Hankel operators $H$ , realised as integral operators on the positive semi-axis. For each value of $E$ , not necessarily in the spectrum of…

math.SP2026

Inverse spectral problems for positive Hankel operators

Alexander Pushnitski, Sergei Treil

A Hankel operator $I^$ 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 $Î…

math.SP2026

SchrÃ¶dinger operators on the half-line with integrable complex potentials

Alexander Pushnitski, FrantiÅ¡ek Å tampach

In our previous work, we introduced the concept of a \emph{spectral pair} for a half-line SchrÃ¶dinger operator with a \emph{complex} bounded potential $q$ , serving as a substitute…

math.SP2025

Sums of projections with random coefficients

Leonid Pastur, Alexander Pushnitski

We study infinite sums \[ {\mathcal P}_{\varkappa}=\sum_{n=-\infty}^\infty \varkappa_n \langle\cdot, Ï_n\rangleÏ_n \] of rank-one projections in a Hilbert space, where $\{Ï_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.SP2025

The Borg-Marchenko uniqueness theorem for complex potentials

Alexander Pushnitski, FrantiÅ¡ek Å tampach

We introduce and study a new theoretical concept of \textit{spectral pair} for a SchrÃ¶dinger operator $H$ in $L^{2} (R_{+})$ with a bounded \textit{complex-valued} potential…