Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Zlotnikov, Ilya"'
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
We study Gabor frames with Hermite window functions. Gr\"ochenig and Lyubarskii provided a sufficient density condition for their frame sets, which leads to what we call the ``safety region". For rectangular lattices and Hermite windows of order 4 an
Externí odkaz:
http://arxiv.org/abs/2403.10503
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
Autor:
Kulikov, Aleksei, Zlotnikov, Ilya
Publikováno v:
Proc. Amer. Math. Soc. 151 (2023), 1637-1641
Let $S_1$ and $S_2$ be disjoint finite unions of parallelepipeds. We describe necessary and sufficient conditions on the sets $S_1,S_2$ and exponents $p$ such that the canonical projection $P$ from $PW_{S_1\cup S_2}^p$ to $PW_{S_1}^p$ is a contractio
Externí odkaz:
http://arxiv.org/abs/2207.09278
Publikováno v:
In Journal of Functional Analysis 1 November 2024 287(9)
Publikováno v:
Journal of Mathematical Analysis and Applications, Volume 515, Issue 2, (2022), 126430
We find the best possible constant $C$ in the inequality $$\|\varphi\|_{L^r}^{\phantom{\frac{p}{r}}}\leq C\|\varphi\|_{L^p}^{\frac{p}{r}}\|\varphi\|_{\mathrm{BMO}}^{1-\frac{p}{r}}$$ for all possible values of parameters $p$ and $r$ such that $1 \le p
Externí odkaz:
http://arxiv.org/abs/2111.05565
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
Autor:
Zlotnikov, Ilya
Publikováno v:
J Fourier Anal Appl 28, 55 (2022)
Let $I=(a,b)\times(c,d)\subset {\mathbb R}_{+}^2$ be an index set and let $\{G_{\alpha}(x) \}_{\alpha \in I}$ be a collection of Gaussian functions, i.e. $G_{\alpha}(x) = \exp(-\alpha_1 x_1^2 - \alpha_2 x_2^2)$, where $\alpha = (\alpha_1, \alpha_2) \
Externí odkaz:
http://arxiv.org/abs/2104.09573