Zobrazeno 1 - 10
of 256
pro vyhledávání: '"A. Olevskiĭ"'
Autor:
Kozma, Gady, Olevskii, Alexander
We survey our recent result that for every continuous function there is an absolutely continuous homeomorphism such that the composition has a uniformly converging Fourier expansion. We mention the history of the problem, orginally stated by Luzin, a
Externí odkaz:
http://arxiv.org/abs/2306.17325
Autor:
Kozma, Gady, Olevskii, Alexander
We show that for every continuous function there exists an absolutely continuous homeomorphism of the circle such that the Fourier series of the composition converges uniformly. This resolves a problem set by N. N. Luzin.
Comment: 55 pages, 2 fi
Comment: 55 pages, 2 fi
Externí odkaz:
http://arxiv.org/abs/2112.00078
We show that there exists a bounded subset of R such that no system of exponentials can be a Riesz basis for the corresponding Hilbert space. An additional result gives a lower bound for the Riesz constant of any putative Riesz basis of the two dimen
Externí odkaz:
http://arxiv.org/abs/2110.02090
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:
Olevskii, Victor
We prove that any non-complete orthonormal system in a Hilbert space can be transformed into a basis by small perturbations.
Externí odkaz:
http://arxiv.org/abs/2008.12877
We prove that every pair of exponential polynomials with imaginary frequencies generates a Poisson-type formula.
Externí odkaz:
http://arxiv.org/abs/2006.12037
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
Autor:
Kozma, Gady, Olevskii, Alexander
We construct a trigonometric series converging to zero everywhere on a subsequence, with coefficients tending to zero. We show that any such series must satisfy that the subsequence is very sparse, and that the support of the related distribution is
Externí odkaz:
http://arxiv.org/abs/1804.06902
Autor:
Lebedev, Vladimir, Olevskii, Alexander
Publikováno v:
Journal of Mathematical Analysis and Applications, 481:2 (2020), 123502, 1-11
We consider the algebras $M_p$ of Fourier multipliers and show that every bounded continuous function $f$ on $\mathbb R^d$ can be transformed by an appropriate homeomorphic change of variable into a function that belongs to $M_p(\mathbb R^d)$ for all
Externí odkaz:
http://arxiv.org/abs/1803.02177
Autor:
Amit, Tomer, Olevskii, Alexander
One says that a pair of sets $(S,Q)$ in $\mathbb{R}$ is 'annihilating' if no function can be concentrated on $S$ while having its Fourier transform concentrated on $Q$. One uses to distinguish between weak and strong annihilation types. It is well kn
Externí odkaz:
http://arxiv.org/abs/1711.04131