University of Illinois Urbana-Champaign

Metric entropies of various function spaces

Strus, Joseph Michael

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https://hdl.handle.net/2142/23623

Description

Title
Metric entropies of various function spaces
Author(s)
Strus, Joseph Michael
Issue Date
1994
Doctoral Committee Chair(s)
Kaufman, Robert
Department of Study
  • Mathematics
  • Engineering, Electronics and Electrical
Discipline
  • Mathematics
  • Engineering, Electronics and Electrical
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Mathematics
  • Engineering, Electronics and Electrical
Language
eng
Abstract
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).
Type of Resource
text
Permalink
http://hdl.handle.net/2142/23623
Copyright and License Information
Copyright 1994 Strus, Joseph Michael

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