BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Daniel Freeman (St Louis University) DTSTART:20230210T150000Z DTEND:20230210T160000Z DTSTAMP:20260404T145130Z UID:BanachWebinars/72 DESCRIPTION:Title: Stable phase retrieval in function spaces\, Part I\nby Daniel Freeman (St Louis University) as part of Banach spaces webinars\n\n\nAbstr act\nLet $(\\Omega\,\\Sigma\,\\mu)$ be a measure space\, and $1\\leq p\\le q \\infty$. 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 \n$$\\inf_{|\\lambda|=1} \\|f-\\lambda g\\|\\leq C\\||f |-|g|\\|.$$\n 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 seve ral applied circumstances\, ranging from crystallography to quantum mechan ics.\n\n\nWe will discuss how problems in phase retrieval are naturally re lated to classical notions in the theory of Banach lattices. Through makin g this connection\, we may apply established methods from the subject to a ttack problems in phase retrieval\, and conversely we hope that the ideas and questions in phase retrieval will inspire a new avenue of research in the theory of Banach lattices.\n\nThis talk is based on joint work with Be njamin Pineau\, Timur Oikhberg\, and Mitchell Taylor.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/72/ END:VEVENT END:VCALENDAR