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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.02798 |
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| _version_ | 1866912742018908160 |
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| author | Shirokov, Nikolai A. Vasin, Andrei V. |
| author_facet | Shirokov, Nikolai A. Vasin, Andrei V. |
| contents | Given a porous compact $K \subset \mathbb{R}^d$ and a continuity modulus $ω$, we prove a quantitative Jackson-Bernstein type theorem on harmonic approximation. That is, a function $f$ belongs to the class $\mathrm{Lip}_ω(K)$ if and only if $f$ can be approximated uniformly on $K$ with a rate of $ω(δ)$ by a function that is harmonic in the $δ$-neighborhood of $K$, provided the uniform estimate $ω(δ)/δ$ on the gradient holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On harmonic approximation of Lipschitz functions on compacts in $\mathbb{R}^d$ Shirokov, Nikolai A. Vasin, Andrei V. Functional Analysis Primary 41A30, Secondary 41A17, 41A63 Given a porous compact $K \subset \mathbb{R}^d$ and a continuity modulus $ω$, we prove a quantitative Jackson-Bernstein type theorem on harmonic approximation. That is, a function $f$ belongs to the class $\mathrm{Lip}_ω(K)$ if and only if $f$ can be approximated uniformly on $K$ with a rate of $ω(δ)$ by a function that is harmonic in the $δ$-neighborhood of $K$, provided the uniform estimate $ω(δ)/δ$ on the gradient holds. |
| title | On harmonic approximation of Lipschitz functions on compacts in $\mathbb{R}^d$ |
| topic | Functional Analysis Primary 41A30, Secondary 41A17, 41A63 |
| url | https://arxiv.org/abs/2508.02798 |