{"paper":{"title":"Nonuniqueness of phase retrieval for three fractional Fourier transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Alessandro Toigo, Claudio Carmeli, Jussi Schultz, Teiko Heinosaari","submitted_at":"2014-11-25T14:20:00Z","abstract_excerpt":"We prove that, regardless of the choice of the angles $\\theta_1,\\theta_2,\\theta_3$, three fractional Fourier transforms $F_{\\theta_1}$, $F_{\\theta_2}$ and $F_{\\theta_3}$ do not solve the phase retrieval problem. That is, there do not exist three angles $\\theta_1$, $\\theta_2$, $\\theta_3$ such that any signal $\\psi\\in L^2(R)$ could be determined up to a constant phase by knowing only the three intensities $|F_{\\theta_1}\\psi|^2$, $|F_{\\theta_2}\\psi|^2$ and $|F_{\\theta_3}\\psi|^2$. This provides a negative argument against a recent speculation by P. Jaming, who stated that three suitably chosen fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6874","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"}