{"paper":{"title":"An Abstract Approach to Weak Convergence of Spectral Shift Functions and Applications to Multi-Dimensional Schr\\\"odinger Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Fritz Gesztesy, Roger Nichols","submitted_at":"2011-11-01T00:51:37Z","abstract_excerpt":"We study the manner in which a sequence of spectral shift functions $\\xi(\\cdot;H_j,H_{0,j})$ associated with abstract pairs of self-adjoint operators $(H_j, H_{0,j})$ in Hilbert spaces $\\cH_j$, $j\\in\\bbN$, converge to a limiting spectral shift function $\\xi(\\cdot;H,H_0)$ associated with a pair $(H,H_0)$ in the limiting Hilbert space $\\cH$ as $j\\to\\infty$ (mimicking the infinite volume limit in concrete applications to multi-dimensional Schr\\\"odinger operators).\n  Our techniques rely on a Fredholm determinant approach combined with certain measure theoretic facts. In particular, we show that pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0096","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"}