Entropy numbers and Marcinkiewicz-type discretization theorem

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.

27 pages

References in corpus (2)

• Integral norm discretization and related problems
• Sampling discretization of integral norms

Cited by in corpus (5)

• Marcinkiewicz-type discretization of $L^p$-norms under the Nikolskii-type inequality assumption
• On optimal recovery in $L_2$
• Bounds on Kolmogorov widths and sampling recovery for classes with small mixed smoothness
• Sampling discretization of integral norms and its application
• Sampling discretization and related problems