{"paper":{"title":"Asymptotics of the number of the interior transmission eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Georgi Vodev, Vesselin Petkov","submitted_at":"2014-03-16T19:00:31Z","abstract_excerpt":"We prove a Weyl asymptotics $N(r) = c r^d + {\\mathcal O}_{\\epsilon}(r^{d - \\kappa + \\epsilon})$, $\\forall\\, 0< \\epsilon \\ll 1$, for the counting function $N(r) = \\sharp\\{\\lambda_j \\in {\\mathbb C} \\setminus \\{0\\}:\\: |\\lambda_j| \\leq r^2\\}$, $r>1$, of the interior transmission eigenvalues (ITE), $\\lambda_j$. Here $0<\\kappa\\leq 1$ is such that there are no (ITE) in the region $\\{\\lambda\\in {\\mathbb C}:\\: |{\\rm Im}\\:\\lambda|\\geq C(| {\\rm Re}\\:\\lambda|+1)^{1-\\frac{\\kappa}{2}}\\}$ for some $C>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3949","kind":"arxiv","version":4},"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"}