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

We construct, on a 2 or 3-dimensional Riemannian manifold, the self-adjoint extensions Δ α,x 0 (αR/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 .

On construit, sur une variété riemannienne X de dimension 2 ou 3, les extensions autoadjointes Δ α,x 0 (αR/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 .

@article{AIF_1982__32_3_275_0,
     author = {Colin De Verdi\`ere, Yves},
     title = {Pseudo-laplaciens. I},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {32},
     number = {3},
     year = {1982},
     pages = {275-286},
     doi = {10.5802/aif.890},
     zbl = {0489.58034},
     mrnumber = {84k:58221},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1982__32_3_275_0}
}
Colin De Verdière, Yves. Pseudo-laplaciens. I. Annales de l'Institut Fourier, Volume 32 (1982) no. 3, pp. 275-286. doi : 10.5802/aif.890. http://www.numdam.org/item/AIF_1982__32_3_275_0/

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