Entropy of Compact Operators with Applications to Landau-Pollak-Slepian Theory and Sobolev Spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912345441173504 |
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| author | Allard, Thomas Bölcskei, Helmut |
| author_facet | Allard, Thomas Bölcskei, Helmut |
| contents | We derive a precise general relation between the entropy of a compact operator and its eigenvalues. It is then shown how this result along with the underlying philosophy can be applied to improve substantially on the best known characterizations of the entropy of the Landau-Pollak-Slepian operator and the metric entropy of unit balls in Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05556 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entropy of Compact Operators with Applications to Landau-Pollak-Slepian Theory and Sobolev Spaces Allard, Thomas Bölcskei, Helmut Functional Analysis We derive a precise general relation between the entropy of a compact operator and its eigenvalues. It is then shown how this result along with the underlying philosophy can be applied to improve substantially on the best known characterizations of the entropy of the Landau-Pollak-Slepian operator and the metric entropy of unit balls in Sobolev spaces. |
| title | Entropy of Compact Operators with Applications to Landau-Pollak-Slepian Theory and Sobolev Spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2406.05556 |