{"paper":{"title":"Spectral determination of analytic axi-symmetric plane domains","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Steve Zelditch","submitted_at":"1999-01-03T18:55:22Z","abstract_excerpt":"Let ${\\cal D}$ denote the class of bounded real analytic plane domains with the symmetry of an ellipse. We prove that if $\\Omega_1, \\Omega_2 \\in {\\cal D}$ and if the Dirichlet spectra coincide, $Spec(\\Omega_1) = Spec(\\Omega_2)$, then $\\Omega_1 = \\Omega_2$ up to rigid motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9901005","kind":"arxiv","version":2},"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"}