57 citations · 121 across the 35 of their papers we have counts for
45 papers
Irregular sampling for hyperbolic secant type functions
Anton Baranov, Yurii Belov
We study Gabor frames in the case when the window function is of hyperbolic secant type, i.e., , . A criterion for half-ir…
Oversampling and Donoho-Logan type theorems in model spaces
Anton Baranov, Philippe Jaming, Karim Kellay +1
The aim of this paper is to extend two results from the Paley--Wiener setting to more generalmodel spaces. The first one is an analogue of the oversampling Shannon sampling formula…
Systems biorthogonal to exponential systems on a finite union of intervals
Anton Baranov, Yurii Belov, Alexander Kuznetsov
We study the properties of a system biorthogonal to a complete and minimal system of exponentials in , where is a finite union of intervals, and show that in the case w…
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…
Cauchy-de Branges spaces, geometry of their reproducing kernels and multiplication operators
Anton Baranov
Cauchy-de Branges spaces are Hilbert spaces of entire functions defined in terms of Cauchy transforms of discrete measures on the plane and generalizing the classical de Branges th…
On Bloch seminorm of finite Blaschke products in the unit disk
Anton D. Baranov, Ilgiz R. Kayumov, Semen R. Nasyrov
We prove that, for any finite Blaschke product in the unit disk, the corresponding Riemann surface over the --plane contains a one-sheeted disk of the radius . Mor…
Estimates for integrals of derivatives of rational functions in multiply connected domains in the plane
A. D. Baranov, I. R. Kayumov
We obtain estimates for integrals of derivatives of rational functions in multiply connected domains in the plane. A sharp order of the growth is found for the integral of the modu…
Complete interpolating sequences for the Gaussian shift-invariant space
Anton Baranov, Yurii Belov, Karlheinz Gröchenig
We give a full description of complete interpolating sequences for the shift-invariant space generated by the Gaussian. As a consequence, we rederive the known density conditions f…
Spectral synthesis for exponentials and logarithmic length
Anton Baranov, Yurii Belov, Aleksei Kulikov
We study hereditary completeness of systems of exponentials on an interval such that the corresponding generating function is small outside of a lacunary sequence of intervals…
Backward shift and nearly invariant subspaces of Fock-type spaces
Alexandru Aleman, Anton Baranov, Yurii Belov +1
We study the structure of the backward shift invariant and nearly invariant subspaces in weighted Fock-type spaces , whose weight is not necessarily radial. We…
New classes of hypercyclic Toeplitz operators
Evgeny Abakumov, Anton Baranov, Stéphane Charpentier +1
We study hypercyclicity of Toeplitz operators in the Hardy space with symbols of the form , where is a rational function and $ϕ\in H^\i…
Spectral theory of rank one perturbations of normal compact operators
Anton Baranov
We construct a functional model for rank one perturbations of compact normal operators acting in a certain Hilbert spaces of entire functions generalizing de Branges spaces. Using…
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…
De Branges spaces and Fock spaces
Anton Baranov, Hélène Bommier-Hato
Relations between two classes of Hilbert spaces of entire functions, de Branges spaces and Fock-type spaces with non-radial weights, are studied. It is shown that any de Branges sp…
On hypercyclic rank one perturbations of unitary operators
Anton Baranov, Vladimir Kapustin, Andrei Lishanskii
Recently, S. Grivaux showed that there exists a rank one perturbation of a unitary operator in a Hilbert space which is hypercyclic. Another construction was suggested later by the…
Univalent functions in model spaces: revisited
Anton Baranov, Yurii Belov, Alexander Borichev +1
Motivated by a problem in approximation theory, we find a necessary and sufficient condition for a model (backward shift invariant) subspace $K_\varTheta = H^2\ominus \varTheta H^2…
Summability properties of Gabor expansions
Anton Baranov, Yurii Belov, Alexander Borichev
We show that there exist complete and minimal systems of time-frequency shifts of Gaussians in which are not strong Markushevich basis (do not admit the spectral…
The Young type theorem in weighted Fock spaces
Anton Baranov, Yurii Belov, Alexander Borichev
We prove that for every radial weighted Fock space, the system biorthogonal to a complete and minimal system of reproducing kernels is also complete under very mild regularity assu…
Synthesable differentiation-invariant subspaces
Anton Baranov, Yurii Belov
We describe differentiation-invariant subspaces of which admit spectral synthesis. This gives a complete answer to a question posed by A.~Aleman and B.~Korenblum. I…
Riesz bases of reproducing kernels in Fock type spaces and de Branges spaces
Anton Baranov, Yurii Belov, Alexander Borichev
We describe the radial Fock type spaces which possess Riesz bases of normalized reproducing kernels and which are (are not) isomorphic to de Branges spaces in terms of the weight f…
De Branges functions of Schroedinger equations
Anton Baranov, Yurii Belov, Alexei Poltoratski
We characterize the Hermite-Biehler (de Branges) functions which correspond to Shroedinger operators with potential on the finite interval. From this characterization one…
Completeness of rank one perturbations of normal operators with lacunary spectrum
Anton D. Baranov, Dmitry V. Yakubovich
Suppose is a compact normal operator on a Hilbert space with certain lacunarity condition on the spectrum (which means, in particular, that its eigenvalues go to…
Geometry of reproducing kernels in model spaces near the boundary
Anton Baranov, Andreas Hartmann, Karim Kellay
We study two geometric properties of reproducing kernels in model spaces where is an inner function in the disc: overcompleteness and existence of uniformly minimalsystem…
Gap Theorem for Separated Sequences without Pain
Anton Baranov, Yurii Belov, Alexander Ulanovskii
We give a simple and straightforward proof of the Gap Theorem for separated sequences by A. Poltoratski and M. Mitkovski using the Beurling--Malliavin formula for the radius of com…