20 citations · 39 across the 10 of their papers we have counts for
8 papers · 1 filter
Localization of zeros in Cauchy-de Branges spaces
Evgeny Abakumov, Anton Baranov, Yurii Belov
We study the class of discrete measures in the complex plain with the following property: up to a finite number, all zeros of any Cauchy transform of the measure (with -dat…
Chui's conjecture in Bergman spaces
Evgeny Abakumov, Alexander Borichev, Konstantin Fedorovskiy
We solve Chui's conjecture on the simplest fractions (i.e., sums of Cauchy kernels with unit coefficients) in weighted (Hilbert) Bergman spaces. Namely, for a wide class of weights…
Krein-type theorems and ordered structure for Cauchy-de Branges spaces
Evgeny Abakumov, Anton Baranov, Yurii Belov
We extend some results of M.G. Krein to the class of entire functions which can be represented as ratios of discrete Cauchy transforms in the plane. As an application we obtain new…
Volterra type operators on growth Fock spaces
Evgeny Abakumov, Evgueni Doubtsov
Let be an unbounded radial weight on , . Using results related to approximation of by entire maps, we investigate Volterra type and weighted compositi…
Approximation by proper holomorphic maps and tropical power series
Evgeny Abakumov, Evgueni Doubtsov
Let be an unbounded radial weight on the complex plane. We study the following approximation problem: find a proper holomorphic map such that $|f…
Localization of zeros for Cauchy transforms
Evgeny Abakumov, Anton Baranov, Yurii Belov
We study the localization of zeros of Cauchy transforms of discrete measures on the real line. This question is motivated by the theory of canonical systems of differential equatio…