Non-positivity of the semigroup generated by the Dirichlet-to-Neumann operator

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Eventually and asymptotically positive semigroups on Banach lattices (2015, background): “Another infinite-dimensional occurrence of eventual positivity was analysed in [17], where it was proven that the semigroup generated by a class of Dirichlet-to-Neumann operators on a disk is eventually positive but not positive in some cases.”
Eventually positive semigroups of linear operators (2015, background): “It is shown in [12] that the eigenvalues of Dλ are of the form”