Kolmogorov widths of balls in mixed norms: the case of rigidity
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909514997956608 |
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| author | Malykhin, Yuri Ryutin, Konstantin |
| author_facet | Malykhin, Yuri Ryutin, Konstantin |
| contents | We describe the set of parameters $(p_1,p_2,q_1,q_2)$ such that the balls $B_{q_1,q_2}^{s,b}$ are rigid in $\ell_{q_1,q_2}^{s,b}$ metric i.e. they are poorly approximated by linear subspaces of dimension $\le (1-\varepsilon)sb$, for large $s, b$. Thus we have settled an important qualitative case in the problem of estimating widths of balls in mixed norms. The proof combines lower bounds from our previous papers and a new construction for the approximation by linear subspaces in the so-called exceptional case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kolmogorov widths of balls in mixed norms: the case of rigidity Malykhin, Yuri Ryutin, Konstantin Functional Analysis We describe the set of parameters $(p_1,p_2,q_1,q_2)$ such that the balls $B_{q_1,q_2}^{s,b}$ are rigid in $\ell_{q_1,q_2}^{s,b}$ metric i.e. they are poorly approximated by linear subspaces of dimension $\le (1-\varepsilon)sb$, for large $s, b$. Thus we have settled an important qualitative case in the problem of estimating widths of balls in mixed norms. The proof combines lower bounds from our previous papers and a new construction for the approximation by linear subspaces in the so-called exceptional case. |
| title | Kolmogorov widths of balls in mixed norms: the case of rigidity |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2502.20152 |