On the existence of large subspaces of C(K) that perform stable phase retrieval

2025/12/08 by García-Sánchez, Enrique, de Hevia, David, Taylor, Mitchell · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #46B42 #46E15 #Advanced Electron Microscopy Techniques and Applications #Advanced X-ray Imaging Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Markov Chains and Monte Carlo Methods

paper · doi:10.48550/arxiv.2512.08114

openalex publication_date 2025/12/08 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28

Abstract

The purpose of this article is to address an open problem posed by Freeman-Oikhberg-Pineau-T.~(Math.~Ann.~2024) regarding the existence of large subspaces of C(K) that perform stable phase retrieval (SPR). We begin by proving that for both the real and complex fields, the space C(K) admits an infinite-dimensional SPR subspace if and only if the second Cantor-Bendixson derivative K'' is nonempty. We then show how to construct ``large" SPR subspaces of C(K), where the size of the subspace depends quantitatively on the number of non-trivial Cantor-Bendixson derivatives that the compact Hausdorff space K possesses.

Citations

• Isometric embeddings into C(K)-spaces doing stable phase retrieval
• On sharp stable recovery from clipped and folded measurements
• The stability of generalized phase retrieval problem over compact groups
• A characterization of complex stable phase retrieval in Banach lattices
• Norm-attaining lattice homomorphisms and renormings of Banach lattices
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• Stable phase retrieval in function spaces
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• Phase retrieval in the general setting of continuous frames for Banach\n spaces
• Phase retrieval in infinite-dimensional Hilbert spaces
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• Saving phase: Injectivity and stability for phase retrieval

Cited by

• Cheeger's Constant for the Gabor Transform and Ripples

Related

• Stable phase retrieval for infinite dimensional subspaces of L₂(ℝ)
• Examples of Hölder-stable Phase Retrieval
• Stable phase retrieval in function spaces
• A characterization of complex stable phase retrieval in Banach lattices
• Isometric embeddings into C(K)-spaces doing stable phase retrieval