{"paper":{"title":"Localization of the interior transmission eigenvalues for a ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Georgi Vodev, Vesselin Petkov","submitted_at":"2016-03-15T09:20:50Z","abstract_excerpt":"We study the localization of the interior transmission eigenvalues (ITEs) in the case when the domain is the unit ball $\\{x \\in {\\mathbb R}^d:\\: |x| \\leq 1\\}, \\: d\\geq 2,$ and the coefficients $c_j(x), \\: j =1,2,$ and the indices of refraction $n_j(x), \\: j =1,2,$ are constants near the boundary $|x| = 1$. We prove that in this case the eigenvalue-free region obtained in [16] for strictly concave domains can be significantly improved. In particular, if $c_j(x), n_j(x), j = 1,2$ are constants for $|x| \\leq 1$, we show that all (ITEs) lie in a strip $\\{ \\lambda \\in {\\mathbb C}:\\:|{\\rm Im}\\: \\lam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04604","kind":"arxiv","version":3},"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"}