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Analysis of the heat kernel of the Dirichlet-to-Neumann operator

Authors:	AFM ter Elst EM Ouhabaz

Institution:	1. Department of Mathematics, University of Auckland, Private bag 92019, Auckland 1142, New Zealand;2. Institut de Mathématiques de Bordeaux, Université Bordeaux 1, UMR 5251, 351, Cours de la Libération, 33405 Talence, France

Abstract:	We prove Poisson upper bounds for the kernel ₍_K_t₎_t_>₀ ${(K_{t})}_{t > 0}$ of the semigroup generated by the Dirichlet-to-Neumann operator if the underlying domain is bounded and has a C^∞ $C^{\infty}$ -boundary. We also prove Poisson bounds for _K_z $K_{z}$ for all z in the right half-plane and for all its derivatives.

Keywords:	35K08 58G11 47B47
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