Projection theorems for intermediate dimensions
| العنوان: | Projection theorems for intermediate dimensions |
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| المؤلفون: | Jonathan M. Fraser, Stuart A. Burrell, Kenneth J. Falconer |
| المساهمون: | EPSRC, University of St Andrews. Pure Mathematics |
| المصدر: | Journal of Fractal Geometry. 8:95-116 |
| بيانات النشر: | European Mathematical Society - EMS - Publishing House GmbH, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Pure mathematics, 28A80, T-NDAS, Dimension (graph theory), Dynamical Systems (math.DS), Fractal, Mathematics - Metric Geometry, Projection (mathematics), Classical Analysis and ODEs (math.CA), FOS: Mathematics, Almost surely, QA Mathematics, Mathematics - Dynamical Systems, QA, Projections, Mathematics, Intermediate dimensions, Capacity, Applied Mathematics, Hausdorff space, Metric Geometry (math.MG), Linear subspace, Mathematics - Classical Analysis and ODEs, Marstrand theorem, Hausdorff dimension, Geometry and Topology, Subspace topology |
| الوصف: | Intermediate dimensions were recently introduced to interpolate between the Hausdorff and box-counting dimensions of fractals. Firstly, we show that these intermediate dimensions may be defined in terms of capacities with respect to certain kernels. Then, relying on this, we show that the intermediate dimensions of the projection of a set $E \subset \mathbb{R}^n$ onto almost all $m$-dimensional subspaces depend only on $m$ and $E$, that is, they are almost surely independent of the choice of subspace. Our approach is based on `intermediate dimension profiles' that are expressed in terms of capacities. We discuss several applications at the end of the paper, including a surprising result that relates the box dimensions of the projections of a set to the Hausdorff dimension of the set. Comment: 17 pages, 0 figures |
| وصف الملف: | application/pdf |
| تدمد: | 2308-1309 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::82f2f38c2aaf6ea1e1cc6079edefc5df https://doi.org/10.4171/jfg/99 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....82f2f38c2aaf6ea1e1cc6079edefc5df |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 23081309 |
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