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Mitchell Taylor (ETH)
Wednesday 01 November 2023, 16:00-17:00
Stable Phase Retrieval in Function Spaces
- 👤 Speaker: Mitchell Taylor (ETH)
- 📅 Date & Time: Wednesday 01 November 2023, 16:00 - 17:00
- 📍 Venue: MR9
Abstract
Let (Ω, Σ, μ) be a measure space, and 1 ≤ p ≤ ∞. A subspace E ⊆ Lp(μ) is said to do stable phase retrieval (SPR) if there exists a constant C ≥ 1 such that for any f, g ∈ E we have
(0.1) inf |λ|=1 ∥f − λg∥ ≤ C∥|f | − |g|∥.
In this case, if |f | is known, then f is uniquely determined up to an unavoidable global phase factor λ; moreover, the phase recovery map is C-Lipschitz. Phase retrieval appears in several applied circumstances, ranging from crystallography to quantum mechanics.
In this talk, I will present some elementary examples of subspaces of Lp(μ) 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, T. Oikhberg and B. Pineau.
Department of Mathematics, ETH Z ̈urich Email address: mitchell.taylor@math.ethz.ch
Series This talk is part of the Analysis Seminar series.
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