Pseudo-laplaciens. I

Yves Colin de Verdière

Annales de l'institut Fourier (1982)

  • Volume: 32, Issue: 3, page 275-286
  • ISSN: 0373-0956

Abstract

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We construct, on a 2 or 3-dimensional Riemannian manifold, the self-adjoint extensions Δ α , x 0 ( α ∈ R / π Z ) 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 .

How to cite

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Colin de Verdière, Yves. "Pseudo-laplaciens. I." Annales de l'institut Fourier 32.3 (1982): 275-286. <http://eudml.org/doc/74552>.

@article{ColindeVerdière1982,
abstract = {On construit, sur une variété riemannienne $X$ de dimension $2$ ou $3$, les extensions autoadjointes $\Delta _\{\alpha ,x_0\}(\alpha \in \{\bf R\}/\pi \{\bf Z\})$ de la restriction du laplacien aux fonctions nulles au voisinage d’un point $x_0$ de $X$. On calcule explicitement les valeurs propres de $\Delta _\{\alpha ,x_0\}$.},
author = {Colin de Verdière, Yves},
journal = {Annales de l'institut Fourier},
keywords = {Riemannian manifolds of dimension 2 or 3; eigenvalues of Laplacian},
language = {fre},
number = {3},
pages = {275-286},
publisher = {Association des Annales de l'Institut Fourier},
title = {Pseudo-laplaciens. I},
url = {http://eudml.org/doc/74552},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Colin de Verdière, Yves
TI - Pseudo-laplaciens. I
JO - Annales de l'institut Fourier
PY - 1982
PB - Association des Annales de l'Institut Fourier
VL - 32
IS - 3
SP - 275
EP - 286
AB - On construit, sur une variété riemannienne $X$ de dimension $2$ ou $3$, les extensions autoadjointes $\Delta _{\alpha ,x_0}(\alpha \in {\bf R}/\pi {\bf Z})$ de la restriction du laplacien aux fonctions nulles au voisinage d’un point $x_0$ de $X$. On calcule explicitement les valeurs propres de $\Delta _{\alpha ,x_0}$.
LA - fre
KW - Riemannian manifolds of dimension 2 or 3; eigenvalues of Laplacian
UR - http://eudml.org/doc/74552
ER -

References

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  2. [2] M. BERGER, P. GAUDUCHON et E. MAZET, Le spectre d'une variété riemannienne, Lecture Notes in Math., 194 (1971), Springer. Zbl0223.53034MR43 #8025
  3. [3] P. CARTIER, Analyse numérique d'un problème de valeurs propres à haute précision (application aux fonctions automorphes), Preprint I.H.E.S., (1978). Zbl0491.10018
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  6. [6] Y. COLIN DE VERDIERE, Une nouvelle démonstration du prolongement méromorphe des séries d'Eisenstein, CRAS, t. 293 (1981), 361-363. Zbl0478.30035MR83a:10038
  7. [7] M. GAFFNEY, Ann. of Math., 60 (1954), 140-145. Zbl0055.40301
  8. [8] GROSSMANN, HOEGH-KROHN, MEBKHOUT, Comm. Math. Phys., 77 (1980), 87-100. 
  9. [9] H. HAAS, Numerische Berechnung..., Diplomarbeit, Heidelberg (1977). 
  10. [10] T. KUBOTA, Elementary theory of Eisenstein series, John Wiley, (1973). Zbl0268.10012MR55 #2759
  11. [11] S. LANG, SL2 (R), Addison-Wesley (1975). 
  12. [12] P. LAX, R. PHILLIPS, Scattering theory for automorphic functions, Annals of Math. Studies, 87 (1976). Zbl0362.10022MR58 #27768
  13. [13] REED, B. SIMON, Methods of modern math. physics, vol. II, Academic Press (1975). Zbl0308.47002
  14. [14] A. VENKOV, Russian Math. Surveys, 34 (1979), 79-153. Zbl0437.10012

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