On Courant's nodal domain property for linear combinations of eigenfunctions
Résumé
We revisit Courant's nodal domain property for linear combinations of eigenfunctions, and propose new, simple and explicit counterexamples for domains in $\mathbb R^2$, $\mathbb S^2$, $\mathbb T^2$, and $\mathbb R^3$, including convex domains.
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