A close look at the entropy numbers of the unit ball of the Reproducing Hilbert Space of isotropic positive definite kernels
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910002583699456 |
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| author | Jordão, T. Gonzalez, K. |
| author_facet | Jordão, T. Gonzalez, K. |
| contents | We present accurate upper and lower bounds for the covering numbers, with explicit constants, of the unit ball for two general classes of Reproducing Kernel Hilbert Space (RKHS) on the unit sphere of $\mathbb{R}^{d+1}$. In both classes, the RKHS is generated by an isotropic continuous positive definite kernel. The upper and lower bounds we present carry precise information about the asymptotic constants, depending on the dimension of the sphere and the monotonic behavior of the Schoenberg/Fourier coefficients of the isotropic kernel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14103 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A close look at the entropy numbers of the unit ball of the Reproducing Hilbert Space of isotropic positive definite kernels Jordão, T. Gonzalez, K. Functional Analysis 47B06, 42C10, 46E22, 41A60 We present accurate upper and lower bounds for the covering numbers, with explicit constants, of the unit ball for two general classes of Reproducing Kernel Hilbert Space (RKHS) on the unit sphere of $\mathbb{R}^{d+1}$. In both classes, the RKHS is generated by an isotropic continuous positive definite kernel. The upper and lower bounds we present carry precise information about the asymptotic constants, depending on the dimension of the sphere and the monotonic behavior of the Schoenberg/Fourier coefficients of the isotropic kernel. |
| title | A close look at the entropy numbers of the unit ball of the Reproducing Hilbert Space of isotropic positive definite kernels |
| topic | Functional Analysis 47B06, 42C10, 46E22, 41A60 |
| url | https://arxiv.org/abs/2304.14103 |