{"paper":{"title":"${L^p}$-theory for Schr\\\"odinger systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdallah Maichine, Abdelaziz Rhandi, Luca Lorenzi, Markus Kunze","submitted_at":"2017-05-09T13:50:58Z","abstract_excerpt":"In this article we study for $p\\in (1,\\infty)$ the $L^p$-realization of the vector-valued Schr\\\"odinger operator $\\mathcal{L}u := \\mathrm{div} (Q\\nabla u) + V u$. Using a noncommutative version of the Dore-Venni theorem due to Monniaux and Pr\\\"uss, we prove that the $L^p$-realization of $\\mathcal{L}$, defined on the intersection of the natural domains of the differential and multiplication operators which form $\\mathcal{L}$, generates a strongly continuous contraction semigroup on $L^p(\\mathbb{R}^d; \\mathbb{R}^m)$. We also study additional properties of the semigroup such as extension to $L^1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03333","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"}