Ellipsoid Methods for Metric Entropy Computation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917669992660992 |
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| author | Allard, Thomas Bölcskei, Helmut |
| author_facet | Allard, Thomas Bölcskei, Helmut |
| contents | We present a new methodology for the characterization of the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. This procedure does not rely on the explicit construction of coverings or packings and provides a unified framework for the derivation of the metric entropy of a wide variety of analytic function classes, such as periodic functions analytic on a strip, analytic functions bounded on a disk, and functions of exponential type. In each of these cases, our results improve upon the best known results in the literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_11066 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ellipsoid Methods for Metric Entropy Computation Allard, Thomas Bölcskei, Helmut Functional Analysis Complex Variables 41A46, 30E10 We present a new methodology for the characterization of the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. This procedure does not rely on the explicit construction of coverings or packings and provides a unified framework for the derivation of the metric entropy of a wide variety of analytic function classes, such as periodic functions analytic on a strip, analytic functions bounded on a disk, and functions of exponential type. In each of these cases, our results improve upon the best known results in the literature. |
| title | Ellipsoid Methods for Metric Entropy Computation |
| topic | Functional Analysis Complex Variables 41A46, 30E10 |
| url | https://arxiv.org/abs/2405.11066 |