{"paper":{"title":"Schatten class conditions for functions of Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Alexander Pushnitski, Rupert L. Frank","submitted_at":"2019-01-17T13:56:03Z","abstract_excerpt":"We consider the difference $f(H_1)-f(H_0)$, where $H_0=-\\Delta$ and $H_1=-\\Delta+V$ are the free and the perturbed Schr\\\"odinger operators in $L^2(\\mathbb R^d)$, and $V$ is a real-valued short range potential. We give a sharp sufficient condition for this difference to belong to a given Schatten class $\\mathbf S_p$, depending on the rate of decay of the potential and on the smoothness of $f$ (stated in terms of the membership in a Besov class). In particular, for $p>1$ we allow for some unbounded functions $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05789","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"}