{"paper":{"title":"The Weyl symbol of Schr\\\"odinger semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jean Nourrigat, Laurent Amour, Lisette Jager","submitted_at":"2013-12-16T12:46:39Z","abstract_excerpt":"In this paper, we study the Weyl symbol of the Schr\\\"odinger semigroup $e^{-tH}$, $H=-\\Delta+V$, $t>0$, on $L^2(\\mathbb{R}^n)$, with nonnegative potentials $V$ in $L^1_{\\rm loc}$. Some general estimates like the $L^{\\infty}$ norm concerning the symbol $u$ are derived. In the case of large dimension, typically for nearest neighbor or mean field interaction potentials, we prove estimates with parameters independent of the dimension for the derivatives $\\partial_x^\\alpha\\partial_\\xi^\\beta u$. In particular, this implies that the symbol of the Schr\\\"odinger semigroups belongs to the class of symbo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4337","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"}