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 ${\mathcal{H}}_n$, which include ordinary phase retrievable frames in ${\mathcal{H}}_n$. 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 ${\mathcal{H}}_n$ 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.

KEYWORDS:

• λ-phase retrievable frame
• frame
• g-phase retrievable frame
• phase coefficient function
• phase retrievable frame

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 32C15
• 42C15