arXiv subjects

Anna Kononova

Publications and source records attributed to Anna Kononova.

7 recordsLinked to original sources

arXiv2026

Uniqueness sets with angular density for spaces of entire functions, III: how to minimize the type

This note is the third part of our work devoted to uniqueness sets for spaces of entire functions. Given a discrete set $Λ$ with angular density $Δ$ with respect to the order $ρ$, satisfying some regularity condition, we show that there exists a type-minimizing measure $Δ_0$ with less than $2ρ$ discrete masses. For the case $ρ=2$, the value of the critical uniqueness type is found in geometric terms.

math.CV↗

arXiv2026

Uniqueness sets with angular density for spaces of entire functions, I. Basics

This is the first part of our work which is devoted to the uniqueness sets for spaces of entire functions. In this part we consider a set $Λ$ with angular density with respect to the order $ρ>0,$ satisfying the Lindelöf condition. We find the value of the critical zero set type for $Λ$ in geometrical terms. We give a necessary and sufficient condition for the coincidence of the critical zero set type and the critical uniqueness set type. At the end of the paper we present an application of our results to random zero sets in Fock-type spaces.

math.CV↗

arXiv2025

Uniqueness sets with angular density for spaces of entire functions, II: $ρ=1$

In this note, which is the second part of a three-part series, we focus on uniqueness sets specifically in the case of spaces of entire functions of exponential type. As in the first part, we consider sets with angular density; however, now we abandon the Lindelöf condition restriction. This part is essentially self-contained and can be read independently of the first one.

math.CV↗

arXiv2022

Random zero sets for Fock type spaces

Given a nondecreasing sequence $Λ=\{λ_n>0\}$ such that $\displaystyle\lim_{n\to\infty} λ_n=\infty,$ we consider the sequence $\mathcal N_Λ:=\left\{λ_ne^{iθ_n},n\in\,\mathbb N\right\}$, where $θ_n$ are independent random variables uniformly distributed on $[0,2π].$ We discuss the conditions on the sequence $Λ$ under which $\mathcal N_Λ$ is a zero set (a uniqness set) of a given weighted Fock space almost surely. The critical density of the sequence $Λ$ with respect to the weight is found.

math.CV↗

arXiv2020

Convergence rate for weighted polynomial approximation on the real line

In this note we study a quantitative version of Bernstein's approximation problem when the polynomials are dense in weighted spaces on the real line completing a result of S.~N.~Mergelyan (1960). We estimate in the logarithmic scale the error of the weighted polynomial approximation of the Cauchy kernel.

math.CA↗

arXiv2019

Notes on the Szego minimum problem. II. Singular measures

In this part, we prove several quantitative results concerning with the Szego minimum problem for classes of measure on the unit circle concentrated on small subsets. As a by-product, we refute one conjecture of Nevai. This note can be read independently from the first one.

math.CV↗

arXiv2019

Notes on the Szego minimum problem. I. Measures with deep zeroes

The classical Szego polynomial approximation theorem states that the polynomials are dense in the space $L^2(ρ)$, where $ρ$ is a measure on the unit circle, if and only if the logarithmic integral of the measure $ρ$ diverges. In this note we give a quantitative version of Szego's theorem in the special case when the divergence of the logarithmic integral is caused by deep zeroes of the measure $ρ$ on a sufficiently rare subset of the circle.

math.CV↗