Remarques sur la conjecture de Weyl

Pierre H. Bérard

Compositio Mathematica (1983)

  • Volume: 48, Issue: 1, page 35-53
  • ISSN: 0010-437X

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Bérard, Pierre H.. "Remarques sur la conjecture de Weyl." Compositio Mathematica 48.1 (1983): 35-53. <http://eudml.org/doc/89586>.

@article{Bérard1983,
author = {Bérard, Pierre H.},
journal = {Compositio Mathematica},
keywords = {wave front set; geodesic flow; Laplace-Beltrami operator; Riemannian polyhedra},
language = {fre},
number = {1},
pages = {35-53},
publisher = {Martinus Nijhoff Publishers},
title = {Remarques sur la conjecture de Weyl},
url = {http://eudml.org/doc/89586},
volume = {48},
year = {1983},
}

TY - JOUR
AU - Bérard, Pierre H.
TI - Remarques sur la conjecture de Weyl
JO - Compositio Mathematica
PY - 1983
PB - Martinus Nijhoff Publishers
VL - 48
IS - 1
SP - 35
EP - 53
LA - fre
KW - wave front set; geodesic flow; Laplace-Beltrami operator; Riemannian polyhedra
UR - http://eudml.org/doc/89586
ER -

References

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  1. [B-B] P. Bérard and G. Besson: Spectres et groupes cristallographiques II: Domaines Sphériques. Ann. Inst. Fourier30: 3 (1980). Zbl0426.35073MR597025
  2. [BD1] P. Bérard: On the wave equation on a Riemannian manifold without conjugate points. Math. Z.155 (1977) 249-276. Zbl0341.35052MR455055
  3. [BD2] P. Bérard: Spectres et groupes cristallographiques I: Domaines Euclidiens. Inventiones Math.58 (1980) 179-199. Zbl0434.35068MR570879
  4. [BI] N. Bourbaki: Groupes et Algèbres de Lie, Chap. 4 à 6, Act. Scient. et Industrielles 1337. Paris: Hermann1968. Zbl0244.22007MR240238
  5. [BL] A. Borel: Compact Clifford-Klein forms of symmetric spaces. Topology2 (1963) 111-122. Zbl0116.38603MR146301
  6. [D-G] J. Duistermaat and V. Guillemin: The spectrum of positive elliptic operators and periodic bicharacteristics. Inventiones Math.29 (1975) 39-79. Zbl0307.35071MR405514
  7. [DT] J. Duistermaat: Fourier integral operators. Lecture Notes, Courant Institute, New York, 1973. Zbl0272.47028MR451313
  8. [GN] V. Guillemin: Lectures on spectral theory for elliptic operators. Duke Math. J.44 (1977) 485-517. Zbl0447.58033MR448452
  9. [GS] D. Gromes: Über die asymptotische Verteilung des Eigenwerte des Laplace-Operators für Gebiete auf der Kugeloberfläche. Math. Z.94 (1966) 110-121. Zbl0146.35002MR199575
  10. [HN] J. Helton: An operator algebra approach to partial differential equations; Propagation of singularities and spectral theory. Indiana University Math. J.26 (1977) 997-1018. Zbl0373.35060MR494325
  11. [KV] N.V. Kuznecov: Asymptotic distribution of the eigenfrequencies of a plane membrane in the case when the variables can be separated. Differential Equations2 (1966) 715-723. Zbl0202.25201MR206524
  12. [ME] R. Melrose: Weyl's conjecture for manifolds with concave boundary. Proceedings of Symposia in Pure Mathematics, vol. 36, Amer. Math. Soc. Providence1980, pp. 254-274. Zbl0436.58024MR573438
  13. [MS] W. Magnus: Non-euclidean tesselations and their groups. Academic Press. Zbl0293.50002
  14. [PTL] Pham The Lai: Meilleures estimations asymptotiques des restes de la fonction spectrale et des valeurs propres relatifs au laplacien. Math. Scand.48 (1981) 5-38. Zbl0466.35060MR621413
  15. [SY1] R. Seeley: A sharp asymptotic remainder estimate for the eigenvalues of the Laplacian in a domain of R3. Adv. in Math.29 (1978) 244-269. Zbl0382.35043MR506893
  16. [SY2] R. Seeley: An estimate near the boundary for the spectral function of the Laplace operator. Amer. J. Math.102 (1980) 869-902. Zbl0447.35029MR590638
  17. [TR] M. Taylor: Pseudo-differential operators. Springer Lecture Notes in Math. n° 416, Springer, 1974. Zbl0289.35001MR442523
  18. (1) A.B. Venkov: Spectral theory of automorphic functions, the Selberg Zeta-function and some problems of analytic number theory and mathematical physics. Russian Math. Surveys34 (1979) 79-153; Zbl0437.10012MR542238
  19. (2) V.Ja. Ivrii:On the second term of the spectral asymptotics for the Laplace-Beltrami operator on manifolds with boundary and for elliptic operators acting on fiberings. Soviet Math. Doklady21 (1980) 300-302; Zbl0448.58024
  20. (3) V. Ja. Ivrii: Second term of the spectral asymptotics expansion of the Laplace-Beltrami operator on manifolds with boundary. Functional Analysis and Applications14 (1980) 98-106. Zbl0453.35068

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