no. 3
Pseudo-laplaciens. I
Annales de l'Institut Fourier, Tome 32 (1982) no. 3, pp. 275-286.

On construit, sur une variété riemannienne X de dimension 2 ou 3, les extensions autoadjointes Δ α,x 0 (α∈R/πZ) de la restriction du laplacien aux fonctions nulles au voisinage d’un point x 0 de X. On calcule explicitement les valeurs propres de Δ α,x 0 .

We construct, on a 2 or 3-dimensional Riemannian manifold, the self-adjoint extensions Δ α,x 0 (α∈R/πZ) of the Laplace operator restricted to the functions vanishing in some neigbhourhood of some point x 0 of X. We compute explicitely the eigenvalues of Δ α,x 0 .

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     author = {Colin De Verdi\`ere, Yves},
     title = {Pseudo-laplaciens. {I}},
     journal = {Annales de l'Institut Fourier},
     pages = {275--286},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {32},
     number = {3},
     year = {1982},
     doi = {10.5802/aif.890},
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     mrnumber = {84k:58221},
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     url = {http://archive.numdam.org/articles/10.5802/aif.890/}
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Colin De Verdière, Yves. Pseudo-laplaciens. I. Annales de l'Institut Fourier, Tome 32 (1982) no. 3, pp. 275-286. doi : 10.5802/aif.890. http://archive.numdam.org/articles/10.5802/aif.890/

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