{"paper":{"title":"Hadamard-type formulas via the Maslov form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Alim Sukhtayev, Yuri Latushkin","submitted_at":"2016-01-27T19:18:42Z","abstract_excerpt":"Given a star-shaped bounded Lipschitz domain $\\Omega\\subset{\\mathbb R}^d$, we consider the Schr\\\"odinger operator $L_{\\mathcal G}=-\\Delta+V$ on $\\Omega$ and its restrictions $L^{\\Omega_t}_{\\mathcal G}$ on the subdomains $\\Omega_t$, $t\\in[0,1]$, obtained by shrinking $\\Omega$ towards its center. We impose either the Dirichlet or quite general Robin-type boundary conditions determined by a subspace ${\\mathcal G}$ of the boundary space $H^{1/2}(\\partial\\Omega)\\times H^{-1/2}(\\partial\\Omega)$, and assume that the potential is smooth and takes values in the set of symmetric $(N\\times N)$ matrices. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07509","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"}