Erratum of “The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent”
Yannick Privat, Mario Sigalotti · ESAIM Control Optimisation and Calculus of Variations · 2009
Firstly, we would like to clarify that domains are, by definition, connected. This is not precisely stated in the definition of Σm in Section 2.1. Secondly, in the proof of Theorem 2.4 we claim that “each Λk(t) converges, as t → +∞, to an eigenvalue of the Laplacian-Dirichlet operator on Ω”. In general, this is not true. The result stated in Theorem 2.4, however, is true and can actually be strengthened as follows. Theorem 2.4. Let (Fn)n∈N, (Pn)n∈N and (Rn)n∈N be as in the statement of Theorem 2.3. Then, for every m ∈ N ∪ {+∞}, a generic Ω ∈ Σm satisfies Pn for every n ∈ N.