A capacity approach to box and packing dimensions of projections of sets and exceptional directions
| العنوان: | A capacity approach to box and packing dimensions of projections of sets and exceptional directions |
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| المؤلفون: | Kenneth J. Falconer |
| المساهمون: | University of St Andrews. Pure Mathematics |
| سنة النشر: | 2019 |
| مصطلحات موضوعية: | Pure mathematics, 28A80, T-NDAS, Hausdorff dimension, Set (abstract data type), symbols.namesake, Projection (mathematics), Dimension (vector space), Mathematics - Metric Geometry, FOS: Mathematics, Projection, QA Mathematics, QA, Mathematics, Box dimension, Capacity, Applied Mathematics, Metric Geometry (math.MG), Linear subspace, Packing dimension, Fourier transform, symbols, Geometry and Topology, Value (mathematics) |
| الوصف: | Dimension profiles were introduced in [8,11] to give a formula for the box-counting and packing dimensions of the orthogonal projections of a set $R^n$ onto almost all $m$-dimensional subspaces. However, these definitions of dimension profiles are indirect and are hard to work with. Here we firstly give alternative definitions of dimension profiles in terms of capacities of $E$ with respect to certain kernels, which lead to the box-counting and packing dimensions of projections fairly easily, including estimates on the size of the exceptional sets of subspaces where the dimension of projection is smaller the typical value. Secondly, we argue that with this approach projection results for different types of dimension may be thought of in a unified way. Thirdly, we use a Fourier transform method to obtain further inequalities on the size of the exceptional subspaces. arXiv admin note: text overlap with arXiv:1711.05316 |
| وصف الملف: | application/pdf |
| اللغة: | English |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1a1050d4a397179cab33cfc999d05b5d http://arxiv.org/abs/1901.11014 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....1a1050d4a397179cab33cfc999d05b5d |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |