Slices of the Takagi function
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913580631195648 |
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| author | Anttila, Roope Bárány, Balázs Käenmäki, Antti |
| author_facet | Anttila, Roope Bárány, Balázs Käenmäki, Antti |
| contents | We show that the Hausdorff dimension of any slice of the graph of the Takagi function is bounded above by the Assouad dimension of the graph minus one, and that the bound is sharp. The result is deduced from a statement on more general self-affine sets, which is of independent interest. We also prove that the Marstrand's slicing theorem on the graph of the Takagi function extends to all slices if and only if the upper pointwise dimension of every projection of the length measure on the $x$-axis lifted to the graph is at least one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08181 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Slices of the Takagi function Anttila, Roope Bárány, Balázs Käenmäki, Antti Classical Analysis and ODEs Primary 28A80, Secondary 28A75, 26A27 We show that the Hausdorff dimension of any slice of the graph of the Takagi function is bounded above by the Assouad dimension of the graph minus one, and that the bound is sharp. The result is deduced from a statement on more general self-affine sets, which is of independent interest. We also prove that the Marstrand's slicing theorem on the graph of the Takagi function extends to all slices if and only if the upper pointwise dimension of every projection of the length measure on the $x$-axis lifted to the graph is at least one. |
| title | Slices of the Takagi function |
| topic | Classical Analysis and ODEs Primary 28A80, Secondary 28A75, 26A27 |
| url | https://arxiv.org/abs/2305.08181 |