Weak Coupling and Spectral Instability for Neumann Laplacians

Jussi Behrndt; Fritz Gesztesy; Henk de Snoo

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arXiv · 2406.18911

Weak Coupling and Spectral Instability for Neumann Laplacians

Jussi Behrndt·Fritz Gesztesy·Henk de Snoo

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Abstract

We prove an abstract criterion on spectral instability of nonnegative selfadjoint extensions of a symmetric operator and apply this to self-adjoint Neumann Laplacians on bounded Lipschitz domains, intervals, and graphs. Our results can be viewed as variants of the classical weak coupling phenomenon for Schr\"odinger operators in $L^2(\mathbb R^n)$ for $n=1,2$.

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BibTeX RIS

Jussi Behrndt, Fritz Gesztesy, Henk de Snoo. 2024-06-27. Weak Coupling and Spectral Instability for Neumann Laplacians. https://arxiv.org/abs/2406.18911

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