The Marcinkiewicz-type discretization theorems

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.

References in corpus (1)

• Constructive sparse trigonometric approximation and other problems for functions with mixed smoothness

Cited by in corpus (2)

• A note on the dispersion of admissible lattices
• Dispersion of the Fibonacci and the Frolov point sets