Entropy numbers and Marcinkiewicz-type discretization theorem

2020/01/28 by Feng Dai, Dai, F., Andriy Prymak +7 · 1 citation
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Approximation and Integration #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.2001.10636

openalex publication_date 2020/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies the behavior of the entropy numbers of classes of functions with bounded integral norms from a given finite dimensional linear subspace. Upper bounds of these entropy numbers in the uniform norm are obtained and applied to establish a Marcinkiewicz type discretization theorem for integral norms of functions from a given finite dimensional subspace.

Cited by

• One-sided discretization inequalities and sampling recovery

Related

• The Marcinkiewicz-type discretization theorems
• Entropy numbers of classes defined by integral operators
• Sampling discretization of integral norms and its application
• Sampling and entropy numbers in the uniform norm
• Bounds for the sampling discretization error and their applications to the universal sampling discretization