{"paper":{"title":"A spectral shift function for Schr\\\"{o}dinger operators with singular interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Fritz Gesztesy, Jussi Behrndt, Shu Nakamura","submitted_at":"2017-10-10T01:03:03Z","abstract_excerpt":"For the pair $\\{-\\Delta, -\\Delta-\\alpha\\delta_\\mathcal{C}\\}$ of self-adjoint Schr\\\"{o}dinger operators in $L^2(\\mathbb{R}^n)$ a spectral shift function is determined in an explicit form with the help of (energy parameter dependent) Dirichlet-to-Neumann maps. Here $\\delta_{\\cal{C}}$ denotes a singular $\\delta$-potential which is supported on a smooth compact hypersurface $\\mathcal{C}\\subset\\mathbb{R}^n$ and $\\alpha$ is a real-valued function on $\\mathcal{C}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03367","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"}