Zobrazeno 1 - 10
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pro vyhledávání: '"ULANOVSKII IN"'
Autor:
Ulanovskii, Alexander, Zlotnikov, Ilya
Let $V^p_\Gamma(\mathcal{G}),1\leq p\leq\infty,$ be the quasi shift-invariant space generated by $\Gamma$-shifts of a function $\mathcal{G}$, where $\Gamma\subset\mathbb{R}$ is a separated set. For several large families of generators $\mathcal{G}$,
Externí odkaz:
http://arxiv.org/abs/2410.08682
Autor:
Ulanovskii, Alexander, Zlotnikov, Ilya
Publikováno v:
Mathematische Annalen (2024)
We introduce two families of generators (functions) $\mathcal{G}$ that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results are proved o
Externí odkaz:
http://arxiv.org/abs/2402.03090
Publikováno v:
Journal of Functional Analysis, Volume 287, Issue 9, 110600, (2024)
We study the space spanned by the integer shifts of a bivariate Gaussian function and the problem of reconstructing any function in that space from samples scattered across the plane. We identify a large class of lattices, or more generally semi-regu
Externí odkaz:
http://arxiv.org/abs/2306.13619
Publikováno v:
Advances in Mathematics, Volume 421, 109016, (2023)
Let $\Gamma$ be a subset of $\{0,1,2,...\}$. We show that if $\Gamma$ has `gaps' then the completeness and frame properties of the system $\{t^ke^{2\pi i nt}: n\in\mathbb{Z},k\in\Gamma\}$ differ from those of the classical exponential systems. This p
Externí odkaz:
http://arxiv.org/abs/2210.00504
Publikováno v:
In Journal of Functional Analysis 1 November 2024 287(9)
Autor:
Ulanovskii, Alexander, Zlotnikov, Ilya
Publikováno v:
International Mathematics Research Notices, Volume 2023, Issue 8, 6329--6363, (2023)
Let $PW_S^1$ be the space of integrable functions on $\mathbb{R}$ whose Fourier transform vanishes outside $S$, where $S = [-\sigma,-\rho]\cup[\rho,\sigma]$, $0<\rho<\sigma$. In the case $\rho>\sigma/2$, we present a complete description of the set o
Externí odkaz:
http://arxiv.org/abs/2108.08093
Every set $\Lambda\subset R$ such that the sum of $\delta$-measures sitting at the points of $\Lambda$ is a Fourier quasicrystal, is the zero set of an exponential polynomial with imaginary frequencies.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/2009.12810
Autor:
Ulanovskii, Alexander, Zlotnikov, Ilya
Publikováno v:
Journal of Functional Analysis, Volume 280, Issue 9, 108962, (2021)
For a wide family of even kernels $\{\varphi_u, u\in I\}$, we describe discrete sets $\Lambda$ such that every bandlimited signal $f$ can be reconstructed from the space-time samples $\{(f\ast\varphi_u)(\lambda), \lambda\in\Lambda, u\in I\}$.
Co
Co
Externí odkaz:
http://arxiv.org/abs/2007.11366
We prove that every pair of exponential polynomials with imaginary frequencies generates a Poisson-type formula.
Externí odkaz:
http://arxiv.org/abs/2006.12037
Publikováno v:
Applied and Computational Harmonic Analysis, Volume 62, (2023), 1-23
Necessary and sufficient conditions are presented for several families of planar curves to form a set of stable sampling for the Bernstein space $\mathcal{B}_{\Omega}$ over a convex set $\Omega \subset \mathbb{R}^2$. These conditions "essentially" de
Externí odkaz:
http://arxiv.org/abs/2005.11193