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SUMMARY:Mitchell A. Taylor (UC Berkeley)
DTSTART:20230217T150000Z
DTEND:20230217T160000Z
DTSTAMP:20260404T145130Z
UID:BanachWebinars/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BanachWebina
 rs/73/">Stable phase retrieval in function spaces\, Part II</a>\nby Mitche
 ll A. Taylor (UC Berkeley) as part of Banach spaces webinars\n\n\nAbstract
 \nLet $(\\Omega\,\\Sigma\,\\mu)$ be a measure space\, and $1\\leq p\\leq \
 \infty$. A subspace $E\\subseteq L_p(\\mu)$ is said to do stable phase ret
 rieval (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 sev
 eral applied circumstances\, ranging from crystallography to quantum mecha
 nics.\n\n\nIn this talk\, I will present some elementary examples of subsp
 aces of $L_p(\\mu)$ which do stable phase retrieval\, and discuss the stru
 cture of this class of subspaces. This is based on a joint work with M. Ch
 rist and B. Pineau\, as well as a joint work with D. Freeman\, B. Pineau a
 nd T. Oikhberg.\n
LOCATION:https://researchseminars.org/talk/BanachWebinars/73/
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