研究希尔伯特空间中连续框架的相位与模长恢复性质
Continuous Approach to Phase (Norm) Retrieval Frames
- 提出连续近里兹基概念并证明其在可逆算子下不变
- 给出相位与模长恢复的等价条件，证明其在扰动下稳定
- 揭示张量积框架与分量间恢复性质的等价性
本文研究希尔伯特空间中连续框架的性质，重点关注相位恢复与模长恢复。引入连续近里兹基概念，并证明其在可逆算子作用下保持不变。给出了连续框架具备相位与模长恢复性质的若干等价条件。研究了相位恢复在扰动下的稳定性。此外，对可分希尔伯特空间的张量积框架进行了分析，建立了分量框架与其张量积之间相位恢复与模长恢复性质的等价关系。
原文摘要 · Abstract (English)
This paper investigates the properties of continuous frames, with a particular focus on phase retrieval and norm retrieval in the context of Hilbert spaces. We introduce the concept of continuous near-Riesz bases and prove their invariance under invertible operators. Some equivalent conditions for phase and norm retrieval property of continuous frames are presented. We study the stability of phase retrieval under perturbations. Furthermore, tensor product frames for separable Hilbert spaces are studied, and we establish the equivalence of phase retrieval and norm retrieval properties between components and their tensor products.
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