Sergei Treil

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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.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.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.