Banach空间中框架的对偶原理

Duality Principles of Frames in Banach Spaces

Gabor理论中的对偶原理(例如Ron-Shen对偶原理和Wexler-Raz双正交关系)在研究Gabor系统时起到了至关重要的作用.对Banach空间中的任意序列,该文定义了仅依赖两组p-Riesz基的一个相关的序列(Riesz-对偶序列),研究它与前一组序列相关的性质.推广了P.G.Casazza、G.Kutyniok和M.C.Lammers在可分Hilbert空间中框架的对偶原理的一些结果.

Duality principles in Gabor theory such as the Ron-Shen duality principle and the Wexler-Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. For each sequence in a Banach space X, we define a corresponding sequence dependent only on two p-Riesz bases in the Banach space X. Then we characterize exactly properties of the first sequence in terms of the associated one. We generate some results that were obtained by P. G. Casazza, G. Kutyniok and M. C. Lammers about duality principles of frames in a separable Hilbert space H.