Yurii Lyubarskii - Academia.edu (original) (raw)

Papers by Yurii Lyubarskii

EMS Press eBooks, May 30, 2018

We prove sharp uniqueness results for a wide class of one-dimensional discrete evolutions. The pr... more We prove sharp uniqueness results for a wide class of one-dimensional discrete evolutions. The proof is based on a construction from the theory of complex Jacobi matrices combined with growth estimates of entire functions.

Journal D Analyse Mathematique, Dec 1, 2001

Functional Analysis and Its Applications, Apr 1, 2007

We consider small oscillations of a system of pairwise interacting particles in an external field... more We consider small oscillations of a system of pairwise interacting particles in an external field near a stable equilibrium. The system is assumed to consist of finitely many channels, i.e., semi-infinite linear chains of particles, attached to a scatterer, which is a finite system of interacting particles. Direct and inverse scattering problems are considered. In particular, an algorithm finding characteristics of the channels on the basis of scattering data is given.

arXiv (Cornell University), Dec 26, 2021

arXiv (Cornell University), Feb 11, 2017

arXiv (Cornell University), Nov 26, 1995

We describe the complete interpolating sequences for the Paley-Wiener spaces L p π (1 < p < ∞) in... more We describe the complete interpolating sequences for the Paley-Wiener spaces L p π (1 < p < ∞) in terms of Muckenhoupt's (A p) condition. For p = 2, this description coincides with those given by Pavlov (1979), Nikol'skii (1980), and Minkin (1992) of the unconditional bases of complex exponentials in L 2 (−π, π). While the techniques of these authors are linked to the Hilbert space geometry of L 2 π , our method of proof is based on turning the problem into one about boundedness of the Hilbert transform in certain weighted L p spaces of functions and sequences.

Russian Mathematical Surveys, Aug 31, 1986

Sampling theory, signal processing, and data analysis, May 1, 2008

Journal de Mathématiques Pures et Appliquées, Aug 1, 2010

We consider Gabor frames generated by a Gaussian function and describe the behavior of the frame ... more We consider Gabor frames generated by a Gaussian function and describe the behavior of the frame constants as the density of the lattice approaches the critical value.

Journal of Approximation Theory, Apr 1, 2005

We consider the problem of reconstruction of functions f from generalized Paley-Wiener spaces in ... more We consider the problem of reconstruction of functions f from generalized Paley-Wiener spaces in terms of their values on complete interpolating sequence {z n }. We characterize the set of data sequences {f (z n)} and exhibit an explicit solution to the problem. Our development involves the solution of a particular* problem.

Journal of Functional Analysis, Feb 1, 2016

Let K ϑ be a model space generated by an inner function ϑ. We study the Schatten class membership... more Let K ϑ be a model space generated by an inner function ϑ. We study the Schatten class membership of embeddings I : K ϑ ֒→ L 2 (µ), µ a positive measure, and of composition operators Cϕ : K ϑ → H 2 (D) with a holomorphic function ϕ : D → D. In the case of onecomponent inner functions ϑ we show that the problem can be reduced to the study of natural extensions of I and Cϕ to the Hardy-Smirnov space E 2 (D) in some domain D ⊃ D. In particular, we obtain a characterization of Schatten membership of Cϕ in terms of Nevanlinna counting function. By example this characterization does not hold true for general ϑ.

Bulletin of The London Mathematical Society, Oct 19, 2011

We study radial behavior of harmonic functions in the unit disk belonging to the Korenblum class.... more We study radial behavior of harmonic functions in the unit disk belonging to the Korenblum class. We prove that functions which admit two-sided Korenblum estimate either oscillate or have slow growth along almost all radii.

Revista Matematica Iberoamericana, Aug 27, 2018

We prove that if a solution of the discrete time-dependent Schrödinger equation with bounded real... more We prove that if a solution of the discrete time-dependent Schrödinger equation with bounded real potential decays fast at two distinct times then the solution is trivial. For the free Shrödinger operator and for operators with compactly supported time-independent potentials a sharp analog of the Hardy uncertainty principle is obtained, using an argument based on the theory of entire functions. Logarithmic convexity of weighted norms is employed in the case of general real-valued time-dependent bounded potentials. In the latter case the result is not optimal.

Comptes Rendus Mathematique, Feb 1, 2007

We investigate Gabor frames based on a linear combination of Hermite functions H n. We derive suf... more We investigate Gabor frames based on a linear combination of Hermite functions H n. We derive sufficient conditions on the lattice Λ ⊆ R 2 such that the Gabor system {e 2πiλ 2 t H n (t − λ 1): λ = (λ 1 , λ 2) ∈ Λ} is a frame. An example supports our conjecture that our conditions are sharp. The main tools are growth estimates for the Weierstrass σ-function and a new type of interpolation problem for entire functions on the Bargmann-Fock space. To cite this article: K.

Journal of Functional Analysis, Oct 1, 1994

Abstract We show that band limited functions can be recovered from their values on certain irregu... more Abstract We show that band limited functions can be recovered from their values on certain irregularly distributed discrete sampling sets as the limits of the piecewise polynomial spline interpolants when the order of the splines goes to infinity. This is an extension of the classical case when the sampling set is a lattice which was considered by Collatz, Quade, Schoenberg, and others.

HAL (Le Centre pour la Communication Scientifique Directe), 2018

We prove that if a solution of the discrete time-dependent Schrödinger equation with bounded time... more We prove that if a solution of the discrete time-dependent Schrödinger equation with bounded time-independent real potential decays fast at two distinct times then the solution is trivial. For the free Shrödinger operator or operators with compactly supported potential a sharp analog of the Hardy uncertainty principle is obtained. The argument is based on the theory of entire functions. Logarithmic convexity of weighted norms is employed for the case of general real-valued bounded potential, for this case the result is not optimal.

$Research paper thumbnail of On the system <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow></mrow><annotation encoding="application/x-tex"></annotation></semantics></math>\{ e^{ - a\lambda _n t} \sin \lambda _n t\} _{n = 1}^\infty <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow></mrow><annotation encoding="application/x-tex"></annotation></semantics></math>$

Functional Analysis and Its Applications, 1986

$Research paper thumbnail of A Hilbert Lemniscate Theorem in \mathbb{C}^2$

Annales de l'Institut Fourier, 2008

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Funkcionalʹnyj analiz i ego priloženiâ, 2007

Complex Variables and Elliptic Equations, Oct 29, 2019

We give a general construction of entire functions in d complex variables that vanish on a lattic... more We give a general construction of entire functions in d complex variables that vanish on a lattice of the form Λ = A(Z + iZ) d for an invertible complex-valued matrix. As an application we exhibit a class of lattices of density > 1 that fail to be a sampling set for the Bargmann-Fock space in C 2. By using an equivalent real-variable formulation, we show that these lattices fail to generate a Gabor frame.