实直线周期子集上的向量值子空间弱Gabor双框架

Vector-valued Subspace Weak Gabor Bi-frames on Periodic Subsets of the Real Line

因其在多路复用技术中的潜在应用,超框架（又称向量值框架）和子空间框架受到了众多数学家和工程专家的关注.弱双框架是希尔伯特空间中双框架的推广.本文研究实直线周期子集上的向量值子空间弱Gabor双框架（WGBFs）,即L2（S,CL）中的WGBFs,其中S是R上的周期子集.利用Zak变换矩阵方法,得到了WGBFs的刻画,它将构造WGBFs的问题归结为设计有限阶Zak变换矩阵;给出了WGBFs的一个例子定理;导出了WGBFs的一个稠密性定理.

Due to their potential applications in multiplexing techniques, superframes （also called vector-valued frames） and subspace frames have interested many mathe- maticians and engineering specialists. A weak bi-frame is a generalization of a bi-frame in a Hilbert space. This paper addresses vector-valued subspace weak Gabor bi-frames （WGBFs） on periodic subsets of the real line, that is, WGBFs for L2（S, CL） with S being periodic subsets of R. Using Zak transform matrix method, we obtain a charac- terization of WGBFs, which reduces constructing WGBFs to designing Zak transform matrices of finite order; present an example theorem of WGBFs; and derive a density theorem for WGBFs.