Level sets of prevalent Hölder functions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911983465398272 |
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| author | Anttila, Roope Bárány, Balázs Käenmäki, Antti |
| author_facet | Anttila, Roope Bárány, Balázs Käenmäki, Antti |
| contents | We study the level sets of prevalent Hölder functions. For a prevalent $α$-Hölder function on the unit interval, we show that the upper Minkowski dimension of every level set is bounded from above by $1-α$ and Lebesgue positively many level sets have Hausdorff dimension equal to $1-α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08520 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Level sets of prevalent Hölder functions Anttila, Roope Bárány, Balázs Käenmäki, Antti Classical Analysis and ODEs Primary 26A16, 28A78, Secondary 26E15, 28A50 We study the level sets of prevalent Hölder functions. For a prevalent $α$-Hölder function on the unit interval, we show that the upper Minkowski dimension of every level set is bounded from above by $1-α$ and Lebesgue positively many level sets have Hausdorff dimension equal to $1-α$. |
| title | Level sets of prevalent Hölder functions |
| topic | Classical Analysis and ODEs Primary 26A16, 28A78, Secondary 26E15, 28A50 |
| url | https://arxiv.org/abs/2402.08520 |