"Stable phase retrieval in function spaces"Taylor, MitchellLet $(\Omega,\Sigma,\mu)$ be a measure space, and $1\leq p\leq \infty$. A subspace $E\subseteq L_p(\mu)$ is said to do \emph{stable phase retrieval (SPR)} if there exists a constant $C\geq 1$ such that for any $f,g\in E$ we have \begin{equation} \inf_{|\lambda|=1} \|f-\lambda g\|\leq C\||f|-|g|\|. \end{equation} In this case, if $|f|$ is known, then $f$ is uniquely determined up to an unavoidable global phase factor $\lambda$; moreover, the phase recovery map is $C$-Lipschitz. Phase retrieval appears in several applied circumstances, ranging from crystallography to quantum mechanics. In this talk, I will present some elementary examples of subspaces of $L_p(\mu)$ which do stable phase retrieval, and discuss the structure of this class of subspaces. This is based on a joint work with M.~Christ and B.~Pineau as well as a joint work with D.~Freeman, T.~Oikhberg and B.~Pineau. |
| https://ps-mathematik.univie.ac.at/e/talks/strobl24_Taylor_2024-02_Abstracts-5.pdf |
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