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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. 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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. 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