"Harmonic analysis, additive combinatorics and geometric measure theory"

“调和分析、加法组合学和几何测度论”

• 批准号: 229818-2012
• 负责人: Laba, Izabella
• 金额: $ 2.19万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=546917
• 关键词: Harmonic; analysis; additive; combinatorics; geometric

A fundamental feature of Euclidean harmonic analysis is the interplay between analysis and geometry. For instance, the geometric features of hypersurfaces in an n-dimensional space, especially curvature and smoothness, are reflected in the ranges of analytic estimates (restriction, maximal estimates) associated with such surfaces. The subject has been studied extensively and in depth, but many fundamental questions still remain open.

欧几里德调和分析的一个基本特征是分析与几何之间的相互作用。例如，n维空间中超曲面的几何特征，特别是曲率和光滑性，反映在与这些曲面相关的分析估计（限制，最大估计）的范围内。这一问题已得到广泛和深入的研究，但许多基本问题仍然悬而未决。