Nombre de valeurs propres d'un opérateur elliptique et polynôme de Hilbert-Samuel

Louis Boutet de Monvel

Séminaire Bourbaki (1978-1979)

  • Volume: 21, page 120-131
  • ISSN: 0303-1179

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Boutet de Monvel, Louis. "Nombre de valeurs propres d'un opérateur elliptique et polynôme de Hilbert-Samuel." Séminaire Bourbaki 21 (1978-1979): 120-131. <http://eudml.org/doc/109931>.

@article{BoutetdeMonvel1978-1979,
author = {Boutet de Monvel, Louis},
journal = {Séminaire Bourbaki},
keywords = {asymptotic behavior of the eigenvalues of an elliptic operator; heat equation approach to the index theorem; symplectic structure; contact manifolds; Toeplitz operators modelled on an elliptic complex; multiplicity of an eigenvalue of a Toeplitz operator; first Betti number; Hilbert-Samuel polynomial of a graded algebra},
language = {fre},
pages = {120-131},
publisher = {Springer-Verlag},
title = {Nombre de valeurs propres d'un opérateur elliptique et polynôme de Hilbert-Samuel},
url = {http://eudml.org/doc/109931},
volume = {21},
year = {1978-1979},
}

TY - JOUR
AU - Boutet de Monvel, Louis
TI - Nombre de valeurs propres d'un opérateur elliptique et polynôme de Hilbert-Samuel
JO - Séminaire Bourbaki
PY - 1978-1979
PB - Springer-Verlag
VL - 21
SP - 120
EP - 131
LA - fre
KW - asymptotic behavior of the eigenvalues of an elliptic operator; heat equation approach to the index theorem; symplectic structure; contact manifolds; Toeplitz operators modelled on an elliptic complex; multiplicity of an eigenvalue of a Toeplitz operator; first Betti number; Hilbert-Samuel polynomial of a graded algebra
UR - http://eudml.org/doc/109931
ER -

References

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  1. [1] M.F. Atiyah and I.M. Singer - The index of elliptic operators I, Ann. Math.87(1968), 484-530. Zbl0164.24001MR236950
  2. [2] L. Boutet De Monvel - On the index of Toeplitz operators of several complex variables, Invent. Math., à paraître. Zbl0398.47018MR520928
  3. [3] L. Boutet De Monvel and V. Guillemin - The spectral theory of Toeplitz operators, à paraître. Zbl0469.47021
  4. [4] L. Boutet De Monvel et J. Sjöstrand - Sur la singularité des noyaux de Bergmann et de Szegö, Astérisque34-35(1976), 123-164. Zbl0344.32010MR590106
  5. [5] Y. Colin De Verdière - Sur le spectre des opérateurs elliptiques à bicaractéristiques toutes périodiques, à paraître Zbl0459.58014
  6. [6] J.J. Duistermaat and V. Guillemin - The spectrum of positive elliptic operators and periodic geodesics, Invent. Math., 29(1975), 184-269. Zbl0307.35071MR423438
  7. [7] A. Melin and J. Sjostrand - Fourier integral operators with complex valued phase functions - dans "Fourier integral operators and Partial Differential Equations", Lecture Notes in Math., n° 459, 120-223, Springer-Verlag. Zbl0306.42007MR431289
  8. [8] A. Weil - Variétés Kählériennes, Hermann, Paris ( 1958). Zbl0137.41103MR111056
  9. [9] A. Weinstein - Asymptotics of eigenvalue clustersfor the Laplacian plus a potential, Duke Math. J., 44(1977), 883-892. Zbl0385.58013MR482878
  10. [10] A. Weinstein - Lectures on symplectic manifolds, Regional conference series in Math., n° 29 ( 1977). Zbl0406.53031MR464312

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