Metric entropies of various function spaces

The metric entropy of a set is a measure of its size in terms of the minimal number of sets of diameter not exceeding 2$\varepsilon$ which cover the set. We calculate the asymptotic order of the metric entropy as \varepsilon \to {\rm 0}\sp{+} for various function spaces. Some spaces we consider are the Sobolov spaces $L\sbsp{1}{p}$((0, 1)) for 1 $<$ $p \leq$ 2, and spaces of smooth functions on certain Cantor-like subsets of (0, 1).

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Strus, Joseph Michael

Contributors dc:contributor

• Kaufman, Robert

• Mathematics
• Engineering, Electronics and Electrical

Statement dc:rights

• Copyright 1994 Strus, Joseph Michael

Language dc:language

eng

Identifier

AAI9503333
(UMI)AAI9503333

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23623