Lipschitz Analysis of g-Phase Retrievable Frames

A g-phase retrievable frame is a \lambda-phase retrievable frame in finite dimensional Hilbert space \mathcal{H}_n, where \lambda is an special function, which is called phase coefficient function. In this paper we study the Lipschitz analysis of the nonlinear map \alpha_{\lambda,{\mathcal{F}}}:\widehat{\mathcal{H}_n}\longrightarrow\mathbb{F}^m, \ \ \ \alpha_{\lambda,{\mathcal{F}}}(\hat{x}):=\begin{bmatrix}\lambda\left( \left\langle {x,f_k}\right\rangle\right)\end{bmatrix}_{۱\leq k\leq m}, where \widehat{\mathcal{H}_n} is the quotient space corresponding to a special equivalence relation on \mathcal{H}_n with respect to phase coefficient function \lambda,  \mathcal{F}=\{f_k\}_{k=۱}^m is a \lambda-phase retrievable frame for \mathcal{H}_n, \mathbb{F}=\mathbb{R} for real Hilbert space \mathcal{H}_n and \mathbb{F}=\mathbb{C} for complex Hilbert space \mathcal{H}_n.

کلیدواژه ها:

Frame ، phase coefficient function ، Phase retrievable frame ، \lambda-Phase retrievable frame ، g-Phase retrievable frame ، Lipschitz continuous function