Kolmogorov widths of an intersection of anisotropic finite-dimensional balls in $l_q^k$ for $1\le q\le 2$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912182836396032 |
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| author | Vasil'eva, A. A. |
| author_facet | Vasil'eva, A. A. |
| contents | In this paper, order estimates for the Kolmogorov $n$-widths of an intersection of an arbitrary family of balls $ν_αB^{\overline{k}}_{\overline{p}_α}$ in $l_q^k$ are obtained for $1\le q\le 2$, $n\le \frac k2$. Here $\overline{p}_α= (p_{α,1}, \, \dots, \, p_{α,d})$, $\overline{k}=(k_1, \, \dots, \, k_d)$, $k=k_1\dots k_d$, $B^{\overline{k}}_{\overline{p}_α}$ is the unit ball with respect to the anisotropic norm given by the vector $\overline{p}_α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05893 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kolmogorov widths of an intersection of anisotropic finite-dimensional balls in $l_q^k$ for $1\le q\le 2$ Vasil'eva, A. A. Functional Analysis In this paper, order estimates for the Kolmogorov $n$-widths of an intersection of an arbitrary family of balls $ν_αB^{\overline{k}}_{\overline{p}_α}$ in $l_q^k$ are obtained for $1\le q\le 2$, $n\le \frac k2$. Here $\overline{p}_α= (p_{α,1}, \, \dots, \, p_{α,d})$, $\overline{k}=(k_1, \, \dots, \, k_d)$, $k=k_1\dots k_d$, $B^{\overline{k}}_{\overline{p}_α}$ is the unit ball with respect to the anisotropic norm given by the vector $\overline{p}_α$. |
| title | Kolmogorov widths of an intersection of anisotropic finite-dimensional balls in $l_q^k$ for $1\le q\le 2$ |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2501.05893 |