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}...
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University of Maragheh
2025-01-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_718214_229cd25355cfe8aba7f136a5459f92f2.pdf |
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| author | Mohammad Ali Hasankhani Fard |
| author_facet | Mohammad Ali Hasankhani Fard |
| author_sort | Mohammad Ali Hasankhani Fard |
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| description | 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 $\alpha_{\lambda,{\mathcal{F}}}:\widehat{\mathcal{H}_n}\longrightarrow\mathbb{F}^m, \ \ \ \alpha_{\lambda,{\mathcal{F}}}(\hat{x}):=\begin{bmatrix}\lambda\left( \left\langle {x,f_k}\right\rangle\right)\end{bmatrix}_{1\leq k\leq m}$, 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 $\lambda$, $\mathcal{F}=\{f_k\}_{k=1}^m$ 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 $\mathcal{H}_n$. |
| format | Article |
| id | doaj-art-020889db97a847598bfc0e21b3462716 |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | University of Maragheh |
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| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-020889db97a847598bfc0e21b34627162025-02-11T05:28:01ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002025-01-0122119320410.22130/scma.2024.2030504.1744718214Lipschitz Analysis of g-Phase Retrievable FramesMohammad Ali Hasankhani Fard0Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.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 $\alpha_{\lambda,{\mathcal{F}}}:\widehat{\mathcal{H}_n}\longrightarrow\mathbb{F}^m, \ \ \ \alpha_{\lambda,{\mathcal{F}}}(\hat{x}):=\begin{bmatrix}\lambda\left( \left\langle {x,f_k}\right\rangle\right)\end{bmatrix}_{1\leq k\leq m}$, 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 $\lambda$, $\mathcal{F}=\{f_k\}_{k=1}^m$ 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 $\mathcal{H}_n$.https://scma.maragheh.ac.ir/article_718214_229cd25355cfe8aba7f136a5459f92f2.pdfframephase coefficient functionphase retrievable frame$\lambda$-phase retrievable frameg-phase retrievable framelipschitz continuous function |
| spellingShingle | Mohammad Ali Hasankhani Fard Lipschitz Analysis of g-Phase Retrievable Frames Sahand Communications in Mathematical Analysis frame phase coefficient function phase retrievable frame $\lambda$-phase retrievable frame g-phase retrievable frame lipschitz continuous function |
| title | Lipschitz Analysis of g-Phase Retrievable Frames |
| title_full | Lipschitz Analysis of g-Phase Retrievable Frames |
| title_fullStr | Lipschitz Analysis of g-Phase Retrievable Frames |
| title_full_unstemmed | Lipschitz Analysis of g-Phase Retrievable Frames |
| title_short | Lipschitz Analysis of g-Phase Retrievable Frames |
| title_sort | lipschitz analysis of g phase retrievable frames |
| topic | frame phase coefficient function phase retrievable frame $\lambda$-phase retrievable frame g-phase retrievable frame lipschitz continuous function |
| url | https://scma.maragheh.ac.ir/article_718214_229cd25355cfe8aba7f136a5459f92f2.pdf |
| work_keys_str_mv | AT mohammadalihasankhanifard lipschitzanalysisofgphaseretrievableframes |