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A Survey on the Hausdorff Dimension of Intersections

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 22 Mar 2023Embargo end date: 01 Jan 2023 English Publisher:MDPI AGJournal:Mathematical and Computational Applications, volume 28, page 49 (eissn: 2297-8747, Copyright policy )
Authors: Mattila Pertti;

doi: 10.3390/mca28020049 , 10.48550/arxiv.2301.13478

arXiv: http://arxiv.org/abs/2301.13478

handle: 10138/357926

A Survey on the Hausdorff Dimension of Intersections

Abstract

Let A and B be Borel subsets of the Euclidean n-space with dimA+dimB>n. This is a survey on the following question: what can we say about the Hausdorff dimension of the intersections A∩(g(B)+z) for generic orthogonal transformations g and translations by z?

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Keywords

T57-57.97, intersection, Applied mathematics. Quantitative methods, Hausdorff dimension; intersection; projection; energy integral; Fourier transform, energy integral, projection, Hausdorff dimension, QA75.5-76.95, Energy integral, Intersection, Mathematics - Classical Analysis and ODEs, Electronic computers. Computer science, Fourier transform, QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Projection, Mathematics

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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Average
Average
Average
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