{"paper":{"title":"Zeta-invariants of the Steklov spectrum for a planar domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Evgeny Malkovich, Vladimir Sharafutdinov","submitted_at":"2014-04-08T13:18:34Z","abstract_excerpt":"The classical inverse problem of recovering a simply connected smooth planar domain from the Steklov spectrum \\cite{E} is equivalent to the problem of recovering, up to a conformal equivalence, a positive function $a\\in C^\\infty({\\mathbb S})$ on the unit circle ${\\mathbb S}=\\{e^{i\\theta}\\}$ from the eigenvalue spectrum of the operator $a\\Lambda_e$, where $\\Lambda_e=(-d^2/d\\theta^2)^{1/2}$. We introduce $2k$-forms $Z_k(a)\\ (k=1,2,\\dots)$ in Fourier coefficients of the function $a$ which are called zeta-invariants. They are uniquely determined by the eigenvalue spectrum of $a\\Lambda_e$. We study"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2117","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"}