A Survey on the Hausdorff Dimension of Intersections

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Mathematical & Computational Applications Pub Date : 2023-01-31 DOI:10.3390/mca28020049

P. Mattila

引用次数: 4

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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关于交叉口Hausdorff维数的研究

设A和B是欧氏n空间的Borel子集，其中dimA+dimB>n。这是对以下问题的一个调查：对于一般正交变换g和z的平移，我们能对交集aå（g（B）+z）的Hausdorff维数说些什么？

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical & Computational Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

自引率

10.50%

发文量

审稿时长

12 weeks

期刊介绍： Mathematical and Computational Applications (MCA) is devoted to original research in the field of engineering, natural sciences or social sciences where mathematical and/or computational techniques are necessary for solving specific problems. The aim of the journal is to provide a medium by which a wide range of experience can be exchanged among researchers from diverse fields such as engineering (electrical, mechanical, civil, industrial, aeronautical, nuclear etc.), natural sciences (physics, mathematics, chemistry, biology etc.) or social sciences (administrative sciences, economics, political sciences etc.). The papers may be theoretical where mathematics is used in a nontrivial way or computational or combination of both. Each paper submitted will be reviewed and only papers of highest quality that contain original ideas and research will be published. Papers containing only experimental techniques and abstract mathematics without any sign of application are discouraged.