{"paper":{"title":"The Morse and Maslov indices for multidimensional Schr\\\"odinger operators with matrix-valued potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.SG"],"primary_cat":"math.SP","authors_text":"Alim Sukhtayev, Christopher K.R.T. Jones, Graham Cox, Yuri Latushkin","submitted_at":"2014-08-05T20:08:02Z","abstract_excerpt":"We study the Schr\\\"odinger operator $L=-\\Delta+V$ on a star-shaped domain $\\Omega$ in $\\mathbb{R}^d$ with Lipschitz boundary $\\partial\\Omega$. The operator is equipped with quite general Dirichlet- or Robin-type boundary conditions induced by operators between $H^{1/2}(\\partial\\Omega)$ and $H^{-1/2}(\\partial\\Omega)$, and the potential takes values in the set of symmetric $N\\times N$ matrices. By shrinking the domain and rescaling the operator we obtain a path in the Fredholm-Lagrangian-Grassmannian of the subspace of $H^{1/2}(\\partial\\Omega)\\times H^{-1/2}(\\partial\\Omega)$ corresponding to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1103","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"}