Zobrazeno 1 - 10
of 422
pro vyhledávání: '"A. A. Ulanovskii"'
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)
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
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
The classical Szeg\"{o}--Kolmogorov Prediction Theorem gives necessary and sufficient condition on a weight $w$ on the unite cirlce $T$ so that the exponentials with positive integer frequences span the weighted space $L^2(T,w)$. We consider the prob
Externí odkaz:
http://arxiv.org/abs/1912.10665
Publikováno v:
In Advances in Mathematics 15 May 2023 421
Publikováno v:
In Applied and Computational Harmonic Analysis January 2023 62:1-23
We construct a Schwartz function $\varphi$ such that for every exponentially small perturbation of integers $\Lambda$, the set of translates $\{\varphi(t-\lambda), \lambda\in\Lambda\}$ spans the space $L^p(R)$, for every $p > 1$. This result remains
Externí odkaz:
http://arxiv.org/abs/1612.00811