Tohoku Mathematical Journal

Spectrum of the Schrödinger operator on a line bundle over complex projective spaces

Ruishi Kuwabara

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 40, Number 2 (1988), 199-211.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178228026

Digital Object Identifier
doi:10.2748/tmj/1178228026

Mathematical Reviews number (MathSciNet)
MR0943819

Zentralblatt MATH identifier
0652.53044

Subjects
Primary: 58G25
Secondary: 35P20: Asymptotic distribution of eigenvalues and eigenfunctions

Citation

Kuwabara, Ruishi. Spectrum of the Schrödinger operator on a line bundle over complex projective spaces. Tohoku Math. J. (2) 40 (1988), no. 2, 199--211. doi:10.2748/tmj/1178228026. https://projecteuclid.org/euclid.tmj/1178228026


Export citation

References

  • [1] M. BERGER, P. GAUDUCHON AND E. MAZET, Le spectre (Tune variete riemannienne, Lec-ture Notes in Math. 194, Springer-Verlag, Berlin-Heidelberg-New York, 1971.
  • [2] Y. COLIN DEVERDIERE, Spectre conjoint d'operateurs pseudo-differentiels qui commuten I. Le cas non integrable, Duke Math. J. 46 (1979), 169-182.
  • [3] J. GASQUI AND H. GOLDSCHMIDT, Une caracterisation des formes exactes de degre 1 su les espaces projectifs, Comment. Math. Helv. 60 (1985), 46-53.
  • [4] V. GUILLEMIN, Some spectral results on rank one symmetric spaces, Advances in Math 28 (1978), 129-137.
  • [5] S. HELGASON, The Radon Transform, Birkhauser, Boston-Basel-Stuttgart, 1980
  • [6] B. KOSTANT, Quantization and unitary representations, Lecture Notes in Math. 170, pp 87-208, Springer-Verlag, Berlin-Heidelberg-New York, 1970.
  • [7] R. KUWABARA, On spectra of the Laplacian on vector bundles, J. Math. Tokushim Univ. 16 (1982), 1-23.
  • [8] R. KUWABARA, Some spectral results for the Laplacian on line bundles over Sn, Com ment. Math. Helv. 59 (1984), 439-458.
  • [9] R. KUWABARA, Spectrum and holonomy of the line bundle over the sphere, Math. Z. 187 (1984), 481-490.
  • [10] R. KUWABARA, Spectrum of the Laplacian on vector bundles over C2re-manifolds, J. Diff Geometry, 27 (1988), 241-258.
  • [11] A. LASCOUX AND M. BERGER, Varietes Kahleriennes compactes, Lecture Notes in Math 154, Springer-Verlag, Berlin-Heidelberg-New York, 1970.
  • [12] A. WEINSTEIN, Asymptotics of eigenvalue clusters for the Laplacian plus a potential, Duke Math. J. 44 (1977), 883-892.
  • [13] R. O. WELLS, JR., Differential Analysis on Complex Manifolds, 2nd ed., Springer-Verlag, Berlin-Heidelberg-New York, 1980.