{"paper":{"title":"Schr\\\"odinger operators on a half-line with inverse square potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Francoise Truc (IF), Hynek Kovarik","submitted_at":"2014-03-14T16:11:30Z","abstract_excerpt":"We consider Schr\\^odinger operators $H_\\alpha$ given by equation (1.1) below. We study the asymptotic behavior of the spectral density $E(H_\\alpha, \\lambda)$ when $\\lambda$ goes to $0$ and the $L^1\\to L^\\infty$ dispersive estimates associated to the evolution operator $e^{-i t H_\\alpha}$. In particular we prove that for positive values of $\\alpha$, the spectral density tends to zero as $\\lambda\\to 0$ with higher speed compared to the spectral density of Schr\\\"odinger operators with a short-range potential $V$. We then show how the long time behavior of $e^{-i t H_\\alpha}$ depends on $\\alpha$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3624","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"}