On the existence of large subspaces of $C(K)$ that perform stable phase retrieval
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910035124158464 |
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| author | García-Sánchez, Enrique de Hevia, David Taylor, Mitchell |
| author_facet | García-Sánchez, Enrique de Hevia, David Taylor, Mitchell |
| contents | The purpose of this article is to address an open problem posed by Freeman-Oikhberg-Pineau-T.~(\textit{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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_08114 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the existence of large subspaces of $C(K)$ that perform stable phase retrieval García-Sánchez, Enrique de Hevia, David Taylor, Mitchell Functional Analysis 46B42, 46E15 The purpose of this article is to address an open problem posed by Freeman-Oikhberg-Pineau-T.~(\textit{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. |
| title | On the existence of large subspaces of $C(K)$ that perform stable phase retrieval |
| topic | Functional Analysis 46B42, 46E15 |
| url | https://arxiv.org/abs/2512.08114 |