Methods of harmonic analysis in convex geometry

凸几何中的调和分析方法

• 批准号: 367804-2009
• 负责人: Yaskin, Vladyslav
• 金额: $ 1.17万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=461027
• 关键词: Methods; harmonic; analysis; convex; geometry

The research project outlined below is concerned with the study of convex bodies and belongs to the area known as geometric tomography. One of the typical questions here is the extent to which knowledge of the size of sections or projections of a convex body yields information about the body itself. The main theme of this proposal is the study of applications of harmonic analysis to convex geometry. One of the earliest such applications goes back to A. Hurwitz's 1901 note on the use of Fourier series to prove the isoperimetric inequality. More recently, A. Koldobsky pioneered a Fourier transform approach to sections of convex bodies, which led, in particular, to an analytic solution to the Busemann-Petty problem.

下面概述的研究项目与凸体的研究有关，属于称为几何层析成像的领域。这里的一个典型问题是，关于凸体的截面或投影大小的知识在多大程度上产生了关于凸体本身的信息。本提案的主要主题是研究调和分析在凸几何中的应用。最早的此类应用之一可以追溯到A. Hurwitz在1901年关于使用傅立叶级数证明等周不等式的注释。最近，a . Koldobsky率先采用傅里叶变换方法来处理凸体的部分，这特别导致了Busemann-Petty问题的解析解。