G-phase retrievable frames

Abstract

In this paper we introduce generalized phase retrievable frames or simply g-phase retrievable frames in real or complex n-dimensional Hilbert space H n , which include ordinary phase retrievable frames in H n . Specifically, a g-phase retrievable frame is a λ-phase retrievable frame, where λ is an special function, which is called phase coefficient function. Using the λ-phase retrievable frames, every vector in H n can be reconstructed up to a constant phase coefficient factor from the action of λ on the its frame coefficients, which can be bounded for bounded phase coefficient functions. We obtain some equivalent conditions to g-phase retrievable frames and we study on stability of special g-phase retrievable frames under small perturbation of their vectors and under small perturbation of their phase coefficient functions.