{"id":568,"date":"2023-01-19T22:07:22","date_gmt":"2023-01-20T06:07:22","guid":{"rendered":"\/wp\/hades\/?p=568"},"modified":"2023-01-19T22:07:22","modified_gmt":"2023-01-20T06:07:22","slug":"stable-phase-retrieval-in-function-spaces","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2023\/01\/19\/stable-phase-retrieval-in-function-spaces\/","title":{"rendered":"Stable phase retrieval in function spaces"},"content":{"rendered":"\n\t\t\t\t\n<p>  The HADES seminar on Tuesday,\u00a0<strong>February 14th<\/strong>\u00a0will be at\u00a0<strong>3:30 pm<\/strong> in <strong>Room 740<\/strong>. <\/p>\n\n\n\n<p><strong>Speaker:<\/strong> Mitchell A. Taylor<\/p>\n\n\n\n<p><strong>Abstract:<\/strong> Let $(\\Omega,\\Sigma,\\mu)$ be a measure space, and $1\\leq p\\leq \\infty$. A subspace $E\\subseteq L_p(\\mu)$ is said to do <em>stable phase retrieval (SPR)<\/em> if there exists a constant $C\\geq 1$ such that for any $f,g\\in E$ we have &nbsp; &nbsp; \\begin{equation}&nbsp; &nbsp; &nbsp; &nbsp;\\inf_{|\\lambda|=1} \\|f-\\lambda g\\|\\leq C\\||f|-|g|\\|.&nbsp; &nbsp; \\end{equation}&nbsp; &nbsp; 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. <\/p>\n\n\n\n<p>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, B. Pineau and T. Oikhberg.<\/p>\n\n\n\n<p><\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0February 14th\u00a0will be at\u00a03:30 pm in Room 740. Speaker: Mitchell A. Taylor Abstract: Let $(\\Omega,\\Sigma,\\mu)$ be a measure space, and $1\\leq p\\leq \\infty$. A subspace $E\\subseteq L_p(\\mu)$ is said to do stable phase retrieval (SPR) if there exists a constant $C\\geq 1$ such that for any $f,g\\in E$ we have &nbsp; [&hellip;]<\/p>\n","protected":false},"author":88,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-568","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/568","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/88"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=568"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/568\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=568"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=568"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=568"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}