Some improved bounds in sampling discretization of integral norms

Autor:	Dai, F., Kosov, E., Temlyakov, V.
Rok vydání:	2022
Předmět:	Mathematics - Functional Analysis Mathematics - Classical Analysis and ODEs Mathematics - Numerical Analysis Mathematics - Probability 42A05 65D30 41A63
Zdroj:	Journal of Functional Analysis 2023
Druh dokumentu:	Working Paper
Popis:	The paper addresses a problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under a standard assumption formulated in terms of the Nikol'skii-type inequality. {In particular, we obtain} some upper bounds on the number of sample points sufficient for good discretization of the integral $L_p$ norms, $1\le p<2$, of functions from finite-dimensional subspaces of continuous functions. Our new results improve upon the known results in this direction. We use a new technique based on deep results of Talagrand from functional analysis. Comment: 46 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.09762 Zobrazit plný text záznamu View this record from Arxiv