框架的局部化

Localization of Frames

中文关键词:  框架  局部化  Banach 框架  密度.

英文关键词:frame  localization  Banach frame  density.

中文摘要:

      Gr\"ochenig 和 Balan, Casazza, Heil, Landau 等人提出了两种框架局部化的概念,这两种局部化在近几年被应用到了Gabor框架, 小波框架和采样定理,得出了许多关于框架的超完备性、冗余度、框架界和密度的关系以及局部化框架的对偶框架的结构方面的重要结果.这些抽象的结果应用到不规则Gabor框架产生了一系列新的结果.采样定理是信号分析中最强有力的基本结果之一,窗口是指数的框架在不规则采样的重构方面有非常重要的应用,一些学者对它的密度已经做过一定的研究.本文第二章将上面提到的

英文摘要:

      Gr\"ochenig and Balan, Casazza, Heil, and Landau introduced the concepts of localization. The concepts were used to Gabor frames, wavelet frames and sampling theorem in recent years. Here they are applied to the frame of exponential windows with the conclusion that the frame of exponential windows is a Banach frame for a kind of Banach spaces, and the conclusion is also obtained about the relationship between frame bounds, frame density, measure and density of indexing set.