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Pavel Gubkin

Publications and source records attributed to Pavel Gubkin.

7 recordsLinked to original sources
arXiv2026

Christoffel functions of measures on the real line with divergent logarithmic integral

Let $σ$ be a Poisson-finite measure on the real line. If its logarithmic integral diverges, then the functions from the classical Hardy space $H^2$ with compactly supported Fourier transform are dense in $L^2(\mathbb{R}, σ)$. We give a quantitative version of this result, adapting the ideas from the 2020 paper by Borichev, Kononova and Sodin, where a similar question was studied in the setting of polynomial approximation.

math.CV↗
arXiv2026

Resonances sets of Schrödinger operators

We prove that resonances of the Schrödinger operator with compactly supported potential can contain arbitrary subset of the angle $\{z: -\text{Im} z > C |\text{Re} z|\}$ that satisfies Blaschke condition. We also establish sufficient conditions for the subsets of wider domains.

math.SP↗
arXiv2025

Direct and inverse spectral continuity for Dirac operators

The half-line Dirac operators with $L^2$-potentials can be characterized by their spectral data. It is known that the spectral correspondence is a homeomorphism: close potentials give rise to close spectral data and vice versa. We prove the first explicit two-sided uniform estimate related to this continuity in the general $L^2$-case. The proof is based on an exact solution of the inverse spectral problem for Dirac operators with $δ$-interactions on a half-lattice in terms of the Schur's algorithm for analytic functions.

math.SP↗
arXiv2022

Dirac operators with exponentially decaying entropy

We prove that the Weyl function of the one-dimensional Dirac operator on the half-line $\mathbb{R}_+$ with exponentially decaying entropy extends meromorphically into the horizontal strip $\{0\ge \mbox{Im}\,z > -δ\}$ for some $δ> 0$ depending on the rate of decay. If the entropy decreases very rapidly then the corresponding Weyl function turns out to be meromorphic in the whole complex plane. In this situation we show that poles of the Weyl function (scattering resonances) uniquely determine the operator.

math.SP↗
arXiv2020

Mate-Nevai-Totik theorem for Krein systems

We prove the Cesàro boundedness of eigenfunctions of the Dirac operator on the half-line with a square-summable potential. The proof is based on the theory of Krein systems and, in particular, on the continuous version of a theorem by A. Mate, P. Nevai and V. Totik from 1991.

math.SP↗