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Absence of eigenvalues of non-self-adjoint Robin Laplacians on the half-space
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By developing the method of multipliers, we establish sufficient conditions which guarantee the total absence of eigenvalues of the Laplacian in the half-space, subject to variable complex Robin boundary conditions. As a further application of this technique, uniform resolvent estimates are derived under the same assumptions on the potential. Some of the results are new even in the self-adjoint setting, where we obtain quantum-mechanically natural conditions.
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On the eigenvalues of the Robin Laplacian with a complex parameter
A dichotomy for complex Robin eigenvalues at large boundary parameter, with new numerical range bounds, a Dirichlet-to-Neumann proof, and interval, rectangle and ball asymptotics.
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