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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 mathematicians 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 characterization 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.
框架 / 弱Gabor双框架 / 向量值框架 / 子空间 {{custom_keyword}} /
frame / weak Gabor bi-frame / vector-valued frame / subspace {{custom_keyword}} /
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国家自然科学基金资助项目（11271037）
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