Box dimension of generalized affine fractal interpolation functions (II)
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929430922788864 |
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| author | Jiang, Lai Ruan, Huo-Jun |
| author_facet | Jiang, Lai Ruan, Huo-Jun |
| contents | Let $f$ be a generalized affine fractal interpolation function with vertical scaling functions. In this paper, we prove the monotonicity of spectral radii of vertical scaling matrices without additional assumptions. We also obtain the irreducibility of these matrices under certain conditions. By these results, we estimate $\mathrm{dim}_B Γf$, the box dimension of the graph of $f$, by the limits of spectral radii of vertical scaling matrices. We also estimate $\mathrm{dim}_B Γf$ directly by the sum function of vertical scaling functions. As an application, we study the box dimension of the graph of a generalized Weierstrass-type function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07786 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Box dimension of generalized affine fractal interpolation functions (II) Jiang, Lai Ruan, Huo-Jun Classical Analysis and ODEs Dynamical Systems Metric Geometry Let $f$ be a generalized affine fractal interpolation function with vertical scaling functions. In this paper, we prove the monotonicity of spectral radii of vertical scaling matrices without additional assumptions. We also obtain the irreducibility of these matrices under certain conditions. By these results, we estimate $\mathrm{dim}_B Γf$, the box dimension of the graph of $f$, by the limits of spectral radii of vertical scaling matrices. We also estimate $\mathrm{dim}_B Γf$ directly by the sum function of vertical scaling functions. As an application, we study the box dimension of the graph of a generalized Weierstrass-type function. |
| title | Box dimension of generalized affine fractal interpolation functions (II) |
| topic | Classical Analysis and ODEs Dynamical Systems Metric Geometry |
| url | https://arxiv.org/abs/2308.07786 |