عنوان Fundamental results on weak phase retrieval عنوان مجله Annals of Functional Analysis نوع پژوهش مقاله چاپ شده کلیدواژهها Hilbert frames , Fusion frame, Finitely full spark , Full spark , Phase retrieval , Norm retrieval چکیده In this manuscript, we answer a list of longstanding open problems on weak phase retrieval including (1) a complete classification of the vectors {xi }i2=1 in R2 that do weak phase retrieval; (2) we show that frames doing weak phase retrieval in Rn must span Rn; (3) we give an example of a set of vectors doing phase retrieval but their orthogonal complement hyperplanes fail weak phase retrieval; (4) we give a classification of weak phase retrievable frames—which makes clear the difference between phase retrieval and weak phase retrieval; (5) we classify when weak phase retrievable frames also do norm retrieval. We then introduce the notion of weak phase retrieval by projections and develop their basic properties. We then look at phase (norm) retrieval by projections. We end with some open problems. We provide numerous examples to show that our results are best possible پژوهشگران پیتر جیکاسازا (نفر اول)، فاتحاکرمی (نفر دوم)، اصغررحیمی (نفر سوم)