ε-Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds
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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/402918 |
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| _version_ | 1849414539028725760 |
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| author | Martin Ehler Frank Filbir |
| author_facet | Martin Ehler Frank Filbir |
| author_sort | Martin Ehler |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-735c4beb303542a8a08cd4f0b7d2471e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-735c4beb303542a8a08cd4f0b7d2471e2025-08-20T03:33:49ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/402918402918ε-Coverings of Hölder-Zygmund Type Spaces on Data-Defined ManifoldsMartin Ehler0Frank Filbir1Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, AustriaFaculty of Mathematics, Technische Universität München, Boltzmannstraße 3, 85748 Garching, GermanyWe 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.http://dx.doi.org/10.1155/2014/402918 |
| spellingShingle | Martin Ehler Frank Filbir ε-Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds Abstract and Applied Analysis |
| title | ε-Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds |
| title_full | ε-Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds |
| title_fullStr | ε-Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds |
| title_full_unstemmed | ε-Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds |
| title_short | ε-Coverings of Hölder-Zygmund Type Spaces on Data-Defined Manifolds |
| title_sort | ε coverings of holder zygmund type spaces on data defined manifolds |
| url | http://dx.doi.org/10.1155/2014/402918 |
| work_keys_str_mv | AT martinehler ecoveringsofholderzygmundtypespacesondatadefinedmanifolds AT frankfilbir ecoveringsofholderzygmundtypespacesondatadefinedmanifolds |