{"paper":{"title":"Stable Gabor phase retrieval for multivariate functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Martin Rathmair, Philipp Grohs","submitted_at":"2019-03-04T07:39:37Z","abstract_excerpt":"In recent work [P. Grohs and M. Rathmair. Stable Gabor Phase Retrieval and Spectral Clustering. Communications on Pure and Applied Mathematics (2018)] the instabilities of the Gabor phase retrieval problem, i.e., the problem of reconstructing a function $f$ from its spectrogram $|\\mathcal{G}f|$, where $$ \\mathcal{G}f(x,y)=\\int_{\\mathbb{R}^d} f(t) e^{-\\pi|t-x|^2} e^{-2\\pi i t\\cdot y} dt, \\quad x,y\\in \\mathbb{R}^d, $$ have been completely classified in terms of the disconnectedness of the spectrogram. These findings, however, were crucially restricted to the onedimensional case ($d=1$) and there"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01104","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}