Sampling discretization of integral norms

Autor:	Dai, F., Prymak, A., Shadrin, A., Temlyakov, V., Tikhonov, S.
Rok vydání:	2020
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. Even though this problem is extremely important in applications, its systematic study has begun recently. In this paper we obtain a conditional theorem for all integral norms $L_q$, $1\le q<\infty$, which is an extension of known results for $q=1$. To discretize the integral norms successfully, we introduce a new technique, which is a combination of probabilistic technique with results on the entropy numbers in the uniform norm. As an application of the general conditional theorem, we derive a new Marcinkiewicz type discretization for the multivariate trigonometric polynomials with frequencies from the hyperbolic crosses. Comment: 16 pages. arXiv admin note: text overlap with arXiv:1703.03743
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2001.09320 Zobrazit plný text záznamu View this record from Arxiv