Reproducing Kernel Hilbert Spaces and entropy Kolmogorov numbers on compact Lie Groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| author | Avetisyan, Zhirayr Ruzhansky, Michael Gonzalez, Karina |
| author_facet | Avetisyan, Zhirayr Ruzhansky, Michael Gonzalez, Karina |
| contents | On a compact Lie group $G$, we consider the reproducing kernel Hilbert space $\mathcal{H}_K$ associated with the integral kernel $K$ of a left-invariant, positive, symmetric, trace class integral operator on $L^2(G)$. We present lower and upper asymptotic estimates for the entropy Kolmogorov numbers (also called covering numbers) for the embedding of $\mathcal{H}_K$ into the space $C(G)$ of continuous functions on $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02305 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reproducing Kernel Hilbert Spaces and entropy Kolmogorov numbers on compact Lie Groups Avetisyan, Zhirayr Ruzhansky, Michael Gonzalez, Karina Functional Analysis On a compact Lie group $G$, we consider the reproducing kernel Hilbert space $\mathcal{H}_K$ associated with the integral kernel $K$ of a left-invariant, positive, symmetric, trace class integral operator on $L^2(G)$. We present lower and upper asymptotic estimates for the entropy Kolmogorov numbers (also called covering numbers) for the embedding of $\mathcal{H}_K$ into the space $C(G)$ of continuous functions on $G$. |
| title | Reproducing Kernel Hilbert Spaces and entropy Kolmogorov numbers on compact Lie Groups |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2602.02305 |