{"paper":{"title":"Schr\\\"odinger type operators with unbounded diffusion and potential terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelaziz Rhandi, Anna Canale, Cristian Tacelli","submitted_at":"2014-06-02T10:27:53Z","abstract_excerpt":"We prove that the realization $A_p$ in $L^p(\\mathbb{R}^N),\\,1<p<\\infty$, of the Schr\\\"odinger type operator $A=(1+|x|^{\\alpha})\\Delta-|x|^{\\beta}$ with domain $D(A_p)=\\{u\\in W^{2,p}(\\mathbb{R}^N): Au\\in L^p(\\mathbb{R}^N)\\}$ generates a strongly continuous analytic semigroup provided that $N>2,\\,\\alpha >2$ and $\\beta >\\alpha -2$. Moreover this semigroup is consistent, irreducible, immediately compact and ultracontractive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0316","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"}