The Marcinkiewicz-type discretization theorems

2017/03/10 by Vladimir Temlyakov, Temlyakov, V. N. · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Approximation and Integration #Numerical Analysis (math.NA) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.1703.03743

openalex publication_date 2017/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. This problem is very important in applications but there is no systematic study of it. We present here a new technique, which works well for discretization of the integral norm. It is a combination of probabilistic technique, based on chaining, with results on the entropy numbers in the uniform norm.

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