Abstract and Applied Analysis

ε-Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds

Martin Ehler and Frank Filbir

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Abstract

We first determine the asymptotes of the ε-covering numbers of Hölder-Zygmund type spaces on data-defined manifolds. Secondly, a fully discrete and finite algorithmic scheme is developed providing explicit ε-coverings whose cardinality is asymptotically near the ε-covering number. Given an arbitrary Hölder-Zygmund type function, the nearby center of a ball in the ε-covering can also be computed in a discrete finite fashion.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 402918, 6 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425047780

Digital Object Identifier
doi:10.1155/2014/402918

Mathematical Reviews number (MathSciNet)
MR3226192

Zentralblatt MATH identifier
07022324

Citation

Ehler, Martin; Filbir, Frank. $\mathbf{\epsilon }$ -Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 402918, 6 pages. doi:10.1155/2014/402918. https://projecteuclid.org/euclid.aaa/1425047780


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