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

collaborators

10 papers

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

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 $q$ , serving as a substitute…

math.SP2025

Sums of projections with random coefficients

Leonid Pastur, Alexander Pushnitski

We study infinite sums \[ {\mathcal P}_{\varkappa}=\sum_{n=-\infty}^\infty \varkappa_n \langle\cdot, ψ_n\rangleψ_n \] 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.…

math.FA2024

Three families of matrices

Alexander Pushnitski

This paper has an expository nature. We compare the spectral properties (such as boundedness and compactness) of three families of semi-infinite matrices and point out similarities…

math.SP2024

Spectral asymptotics for a family of arithmetical matrices and connection to Beurling primes

Titus Hilberdink, Alexander Pushnitski

We consider the family of arithmetical matrices given explicitly by $E = {\frac{[ n , m ] ^{t}}{( nm ) ^{(ρ + t) /2}}}_{n, m = 1}^{\infty}$ where $[n, m]$ is the least common multiple of…

math.FA2020★ 4 cited

The spectrum of some Hardy kernel matrices

Ole Fredrik Brevig, Karl-Mikael Perfekt, Alexander Pushnitski

For $α > 0$ we consider the operator $K_{α} : ℓ^{2} \to ℓ^{2}$ corresponding to the matrix \[\left(\frac{(nm)^{-\frac{1}{2}+α}}{[\max(n,m)]^{2α}}\right)_{n,m=1}^\infty.\] By int…