ABSTRACT

The primary purpose of this paper is to discuss phase-retrievable g-frames and exact phase-retrievable g-frames. Firstly, some characterizations of phase-retrievable g-frames are discussed. And some necessary and sufficient conditions to make g-frames phase-retrievable g-frames can be obtained. Furthermore, we find that for a phase-retrievable g-frame, its canonical dual g-frame is also phase-retrievable. With the help of these results, the stability of phase-retrievability is studied. More specifically, a phase-retrievable g-frame is still phase-retrievable after a small disturbance. And an easy way to construct a phase-retrievable g-frame by using a phase-retrievable frame will be found. Then a special phase-retrievable g-frame, the exact phase-retrievable g-frame is introduced. Similar to the phase-retrievable g-frame, some necessary and sufficient conditions to make g-frames exact phase-retrievable are studied, and some characterizations of exact phase-retrievable g-frames can be obtained.

摘要

本文的主要目的是讨论可相位恢复的g帧和精确的可相位恢复的g帧。首先，讨论了相位可恢复g帧的一些特征。并且可以获得使g帧可相位恢复的g帧的一些必要和充分条件。此外，我们发现，对于可相位恢复的g帧，其经典双g帧也是可相位恢复的。借助这些结果，研究了相可恢复性的稳定性。更具体地，在小干扰之后，可相位恢复的g帧仍然是可相位恢复的。并且将找到通过使用可相位恢复的帧来构造可相位恢复的g帧的简单方法。然后介绍了一个特殊的相位可恢复g帧，即精确的相位可恢复g帧。与相位可检索的g帧相似，