{"paper":{"title":"Dispersive Estimates for higher dimensional Schr\\\"odinger Operators with threshold eigenvalues I: The odd dimensional case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Goldberg, William R. Green","submitted_at":"2014-09-22T20:02:21Z","abstract_excerpt":"We investigate $L^1(\\mathbb R^n)\\to L^\\infty(\\mathbb R^n)$ dispersive estimates for the Schr\\\"odinger operator $H=-\\Delta+V$ when there is an eigenvalue at zero energy and $n\\geq 5$ is odd. In particular, we show that if there is an eigenvalue at zero energy then there is a time dependent, rank one operator $F_t$ satisfying $\\|F_t\\|_{L^1\\to L^\\infty} \\lesssim |t|^{2-\\frac{n}{2}}$ for $|t|>1$ such that $$\\|e^{itH}P_{ac}-F_t\\|_{L^1\\to L^\\infty} \\lesssim |t|^{1-\\frac{n}{2}},\\qquad\\textrm{ for } |t|>1.$$ With stronger decay conditions on the potential it is possible to generate an operator-valued "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6323","kind":"arxiv","version":3},"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"}