Stable Phase Retrieval in Function Spaces

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• Mitchell Taylor (ETH)
• Wednesday 01 November 2023, 16:00-17:00
• MR9.

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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

This talk is part of the Analysis Seminar series.

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