{"paper":{"title":"Analyticity of the Dirichlet-to-Neumann semigroup on continuous functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.F.M. ter Elst, E.M. Ouhabaz","submitted_at":"2017-07-24T19:36:29Z","abstract_excerpt":"Let $\\Omega$ be a bounded open subset with $C^{1+\\kappa}$-boundary for some $\\kappa > 0$. Consider the Dirichlet-to-Neumann operator associated to the elliptic operator $- \\sum \\partial_l ( c_{kl} \\, \\partial_k ) + V$, where the $c_{kl} = c_{lk}$ are H\\\"older continuous and $V \\in L_\\infty(\\Omega)$ are real valued. We prove that the Dirichlet-to-Neumann operator generates a $C_0$-semigroup on the space $C(\\partial \\Omega)$ which is in addition holomorphic with angle $\\frac{\\pi}{2}$. We also show that the kernel of the semigroup has Poisson bounds on the complex right half-plane. As a consequen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07718","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"}