Sergei Treil

activity

20222026

collaborators

5 papers

math.SP2026

Analysis of the Singular Spectrum for General Perturbations

Constanze Liaw, Eero Saksman, Sergei Treil

We investigate the behavior of the singular spectrum of self-adjoint operators under families of Hermitian perturbations, even non-compact ones. Under mild assumptions we have the…

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

Unbounded integral Hankel operators

Alexander Pushnitski, Sergei Treil

For a wide class of unbounded integral Hankel operators on the positive half-line, we prove essential self-adjointness on the set of smooth compactly supported functions.

math.FA2022

A Dynamical System Approach to the Inverse Spectral Problem for Hankel Operators: A Model Case

Zhehui Liang, Sergei Treil

We present an alternative proof of the result by P. Gerard and S. Grellier, stating that given two real sequences $(λ_{n})_{n = 1}^{\infty}$ , $(μ_{n})_{n = 1}^{\infty}$ satisfying the intertwi…