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SUMMARY:Stable Phase Retrieval in Function Spaces - Mitchell Taylor (ETH)
DTSTART:20231101T160000Z
DTEND:20231101T170000Z
UID:TALK207964@talks.cam.ac.uk
CONTACT:27311
DESCRIPTION:Let (Ω\, Σ\, μ) be a measure space\, and 1 ≤ p ≤ ∞. 
 A subspace E ⊆ Lp(μ) is said to do stable\nphase retrieval (SPR) if the
 re exists a constant C ≥ 1 such that for any f\, g ∈ E we have\n\n(0.1
 ) inf\n|λ|=1 ∥f − λg∥ ≤ C∥|f | − |g|∥.\n\n\nIn this case\,
  if |f | is known\, then f is uniquely determined up to an unavoidable glo
 bal phase factor\nλ\; moreover\, the phase recovery map is C-Lipschitz. P
 hase retrieval appears in several applied\ncircumstances\, ranging from cr
 ystallography to quantum mechanics.\n\nIn this talk\, I will present some 
 elementary examples of subspaces of Lp(μ) which do stable phase\nretrieva
 l\, and discuss the structure of this class of subspaces. This is based on
  a joint work with\nM. Christ and B. Pineau as well as a joint work with D
 . Freeman\, T. Oikhberg and B. Pineau.\n\n\nDepartment of Mathematics\, ET
 H Z ̈urich\nEmail address: mitchell.taylor@math.ethz.ch
LOCATION:MR9
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