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Copyright © 2014 Martin Ehler and Frank Filbir. Martin Ehler et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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

Details

Title
[epsilon] -Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds
Author
Ehler, Martin; Filbir, Frank
Publication year
2014
Publication date
2014
Publisher
John Wiley & Sons, Inc.
ISSN
10853375
e-ISSN
16870409
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
1552816077
Copyright
Copyright © 2014 Martin Ehler and Frank Filbir. Martin Ehler et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.