论文标题
feichtinger猜想，$ r_ \ varepsilon $ - 注射和织布工的猜想
Feichtinger Conjectures, $R_\varepsilon$-Conjectures and Weaver's Conjectures for Banach spaces
论文作者
论文摘要
来自二十年著名的fe夫构想的动机，$ r_ \ r_ \ varepsilon $ - 注射器和韦弗对希尔伯特空间的猜想（以及马库斯，斯皮尔曼和斯里瓦斯塔瓦的解决方案），我们为p-appproximate schauder frameer and $ r _ r _ $ r r _ $ r \ r \ riilon $ r \ r \ r \ r \ r \ r \ r \ r \ r \ r \ r \ riilon undifeer the Infecture the $ r。 Akemann-Weaver的猜想是Banach空间。我们还根据Hilbert Space的Casazza的结果来对P-Approximate Schauder框架进行猜想。我们陈述了基于希尔伯特空间框架的基本不平等，以及希尔伯特太空框架的扩展问题，对p-相关的Schauder框架的猜想和问题。基于Hilbert空间的Riesz基础的Kothe-lorch定理，我们为Banach空间的P- Apploximate Riesz基地提出了一个问题。我们为Banach空间的P-Approximate Schauder框架制定动态抽样问题。我们为BANACH空间的P-Approximate Schauder框架询问阶段检索问题和规范检索问题。我们还为连续的p- Appleximate Schauder框架提出了离散化问题。
Motivated from two decades old famous Feichtinger conjectures for frames, $R_\varepsilon$-conjecture and Weaver's conjecture for Hilbert spaces (and their solution by Marcus, Spielman, and Srivastava), we formulate Feichtinger conjectures for p-approximate Schauder frames, $R_\varepsilon$-conjecture, Weaver's conjectures and Akemann-Weaver conjectures for Banach spaces. We also formulate conjectures on p-approximate Schauder frames based on the results of Casazza for frames for Hilbert spaces. We state conjectures and problems for p-approximate Schauder frames based on fundamental inequality for frames for Hilbert spaces and scaling problem for Hilbert space frames. Based on Kothe-Lorch theorem for Riesz bases for Hilbert spaces, we formulate a problem for p-approximate Riesz bases for Banach spaces. We formulate dynamical sampling problem for p-approximate Schauder frames for Banach spaces. We ask phase retrieval problem and norm retrieval problem for p-approximate Schauder frames for Banach spaces. We also formulate discretization problem for continuous p-approximate Schauder frames.
