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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
Universal Sampling Discretization
F. Daia, V. N. Temlyakovbcde a Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
b University of South Carolina, Columbia, USA
c Steklov Institute of Mathematics, Moscow, Russia
d Lomonosov Moscow State University, Moscow, Russia
e Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia
Аннотация:
Let $X_N$ be an $N$-dimensional subspace of $L_2$ functions on a probability space $(\Omega , \mu )$ spanned by a uniformly bounded Riesz basis $\Phi _N$. Given an integer $1\le v\le N$ and an exponent $1\le p\le 2$, we obtain universal discretization for the integral norms $L_p(\Omega ,\mu )$ of functions from the collection of all subspaces of $X_N$ spanned by $v$ elements of $\Phi _N$ with the number $m$ of required points satisfying $m\ll v(\log N)^2(\log v)^2$. This last bound on $m$ is much better than previously known bounds which are quadratic in $v$. Our proof uses a conditional theorem on universal sampling discretization, and an inequality of entropy numbers in terms of greedy approximation with respect to dictionaries.
Поступила в редакцию: 25.04.2023
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