Harmonic and functional analysis of wavelet and frame expansions

小波和框架展开的调和和泛函分析

• 批准号: 1265711
• 负责人: Marcin Bownik
• 金额: $ 13.2万
• 依托单位: University of Oregon Eugene
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-01 至 2017-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1265711&HistoricalAwards=false
• 关键词: Harmonic; functional; analysis; wavelet; frame

This mathematics research project by Marcin Bownik is focused on the investigation of the harmonic - and functional-analytic aspects of the mathematical theory of multi- dimensional wavelet and frame expansions. One of the main research directions of the project is the development of techniques for the construction of well-localized orthogonal wavelets for large classes of non-isotropic expansive dilations. A closely related complementary topic is the study of non-isotropic analogues of classical function spaces associated to expansive dilations. Another direction of the project is the construction of frames with desired properties such as with prescribed norms and frame operator. This line of research is closely related with the infinite dimensional generalizations of the Schur- Horn theorem.This mathematics research project by Marcin Bownik explores the mathematical theory of wavelet and frame expansions. In recent years, wavelet and frame theory has found many applications to a wide range of disciplines including applied and computational harmonic analysis, signal processing and data compression. Some well -known examples where wavelets are a key tool include the JPEG 2000 digital image standard and fingerprint compression for data storage. This project aims to further the mathematical theory that provides the foundation for further applications of wavelets and frames.

这个数学研究项目的马尔辛Bownik是集中在调查的谐波和功能分析方面的数学理论的多维小波和框架的扩展。该项目的主要研究方向之一是为大类非各向同性膨胀膨胀构造良好的局部化正交小波的技术的发展。一个密切相关的补充主题是研究与膨胀膨胀相关的经典函数空间的非各向同性类似物。该项目的另一个方向是建造具有所需特性的框架，例如具有规定的规范和框架操作员。这条研究路线与Schur- Horn定理的无限维推广密切相关。Marcin Bownik的这个数学研究项目探索了小波和框架展开的数学理论。近年来，小波和框架理论在应用和计算谐波分析、信号处理和数据压缩等学科中得到了广泛的应用。小波是关键工具的一些众所周知的例子包括JPEG 2000数字图像标准和用于数据存储的指纹压缩。该项目旨在进一步的数学理论，为小波和框架的进一步应用提供基础。