The Marcinkiewicz-Type Discretization Theorems

By Vladimir N. Temlyakov. Constructive approximation, 2017

63 citations recorded by the source corpus.

This 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, and results on the entropy numbers in the uniform norm.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/edcd2e5ef5389070fa1b225698f75cf9ec237f5a