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SUMMARY:Stable phase retrieval in function spaces
DTSTART:20240326T141500
DTEND:20240326T153000
DTSTAMP:20260407T064445Z
UID:2aaca39097ea84f812b4133580588d7b56b4d31cda319f06fb1cb68f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Mitchell Taylor (ETHZ)\n   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 \\emph{stable phase retrieval (SPR)} if there exists 
 a constant $C\\geq 1$ such that for any $f\,g\\in E$ we have \n    \\be
 gin{equation}\n       \\inf_{|\\lambda|=1} \\|f-\\lambda g\\|\\leq C\\
 ||f|-|g|\\|.\n    \\end{equation}\n    In this  case\, if $|f|$ is kn
 own\, then $f$ is uniquely determined up to an unavoidable global phase fa
 ctor $\\lambda$\; moreover\, the phase recovery map is $C$-Lipschitz. Phas
 e retrieval appears in several applied circumstances\, ranging from crysta
 llography to quantum mechanics.\n\nIn this talk\, I will present some elem
 entary examples of subspaces of $L_p(\\mu)$ which do stable phase retrieva
 l and discuss the structure of this class of subspaces. In particular\, I 
 will explain how SPR connects to $\\Lambda(p)$-set theory\, which is a cla
 ssical topic in the intersection of number theory and harmonic analysis. 
 \n\nThe material in this talk is based on joint work with M.~Christ and B.
 ~Pineau as well as with D.~Freeman\, T.~Oikhberg and B.~Pineau. 
LOCATION:MA A1 10 https://plan.epfl.ch/?room==MA%20A1%2010
STATUS:CONFIRMED
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