The Marcinkiewicz-Type Discretization Theorems

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...

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Bibliographic Details
Published inConstructive approximation Vol. 48; no. 2; pp. 337 - 369
Main Author Temlyakov, V. N.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2018
Springer Nature B.V
Subjects
Analysis
Discretization
Integrals
Mathematics
Mathematics and Statistics
Norms
Numerical Analysis
Primary 41A65
Sparse approximation
Discretization
Secondary 42A10
46B20
Chaining
Entropy
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0176-4276
1432-0940
DOI:10.1007/s00365-018-9446-2