{"paper":{"title":"Upper bound for the counting function of interior transmission eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Mouez Dimassi, Vesselin Petkov","submitted_at":"2013-08-12T15:37:57Z","abstract_excerpt":"For the complex interior transmission eigenvalues (ITE) we study for small $\\theta > 0$ the counting function $$N(\\theta, r) = #\\{\\lambda \\in \\C:\\: \\lambda \\: {\\rm is} \\: {\\rm (ITE)},\\: |\\lambda| \\leq r, \\: 0 \\leq \\arg \\lambda \\leq \\theta\\}.$$ We obtain for fixed $\\theta > 0$ an upper bound $N(\\theta, r) \\leq C r^{n/2}, \\: r \\geq r(\\theta).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2594","kind":"arxiv","version":5},"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"}