Skip to main content

Decay of eigenfunctions on Riemannian manifolds

  • 903 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1339)

Keywords

  • Riemannian Manifold
  • Ricci Curvature
  • Essential Spectrum
  • Decay Condition
  • Complete Riemannian Manifold

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Agmon, S., Lectures on exponential decay of solutions of second order elliptic equations, bounds on eigenfunctions of n-body Schrödinger operators, Princeton University Press, Princeton, N.J., 1982.

    MATH  Google Scholar 

  2. Bardos, C. and Merigot, M., Asymptotic decay of the solution of a second order elliptic equation in an unbounded domain, applications to the spectral properties of a Hamiltonian, Proceedings of the Royal Society, Edinburgh, 76A (1977), 323–344.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Cheeger, J., Gromov, M., and Taylor, M., Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geometry, 17 (1982), 15–53.

    MathSciNet  MATH  Google Scholar 

  4. Cheng, S. Y. and Yau, S. T., Differential equations on Riemannian manifolds and their geometric applications, Communications on Pure and Applied Mathematics, 28 (1975), 333–354.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Davies, E. B., Simon, Barry, and Taylor, M., Lp spectral theory of Kleinian groups, Preprint.

    Google Scholar 

  6. Donnelly, H., Eigenforms of the Laplacian on complete Riemannian manifolds, Communications in Partial Differential Equations, 9 (1984), 1299–1321.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Donnelly, H., On the essential spectrum of a complete Riemannian manifold, Topology, 20 (1981), 1–14.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Donnelly, H., Lower bounds for eigenfunctions on Riemannian manifolds, Preprint.

    Google Scholar 

  9. Fabes, E., Jerison, D., and Kenig, C., Necessary and sufficient conditions for absolute continuity of elliptic-harmonic measure, Annals of Math., 119 (1984), 121–141.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Glazeman, I. M., Direct methods of qualitative spectral analysis of singular differential operators, Daniel Davey, N.Y., 1965.

    Google Scholar 

  11. Greene, R. and Wu, H., Function theory on manifolds which possess a pole, Springer-Verlag Lecture Notes in Mathematics, Vol. 699, Berlin, Heidelberg, N.Y., 1979.

    Google Scholar 

  12. Hartman, P., Ordinary Differential Equations, Wiley, N.Y., 1964.

    MATH  Google Scholar 

  13. Reed, M. and Simon, B., Methods of Modern Mathematical Physics IV, Analysis of Operators, Academic Press, N.Y., 1978.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Donnelly, H. (1988). Decay of eigenfunctions on Riemannian manifolds. In: Sunada, T. (eds) Geometry and Analysis on Manifolds. Lecture Notes in Mathematics, vol 1339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083050

Download citation

  • DOI: https://doi.org/10.1007/BFb0083050

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50113-8

  • Online ISBN: 978-3-540-45930-9

  • eBook Packages: Springer Book Archive