{"paper":{"title":"Radial positive definite functions and spectral theory of the Schr\\\"odinger operators with point interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"M. Malamud, N. Goloshchapova, V. Zastavnyi","submitted_at":"2017-01-23T15:05:46Z","abstract_excerpt":"We complete the classical Schoenberg representation theorem for radial positive definite functions. We apply this result to study spectral properties of self-adjoint realizations of two- and three-dimensional Schr\\\"odinger operators with point interactions on a finite set. In particular, we prove that any realization has purely absolutely continuous non-negative spectrum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06436","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"}