New properties of phase-retrievable g-frames and exact phase-retrievable g-frames

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.

Keywords:

• Phase-retrievable
• exact phase-retrievable
• g-frames

2010 Mathematics Subject Classifications:

• Primary 42C15
• Secondary 46C07

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The support provided by China Scholarship Council (CSC) [201906070102] during a visit of 'He Miao' to NUS is acknowledged. And this work is supported by the Applied Basic Research Programs Department of Science and Technology of Sichuan Province [2019YJ0185].