Spectral analysis of non-compact manifolds using commutator methods

P. D. Hislop

Séminaire Équations aux dérivées partielles (Polytechnique) (1987-1988)

  • page 1-11

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Hislop, P. D.. "Spectral analysis of non-compact manifolds using commutator methods." Séminaire Équations aux dérivées partielles (Polytechnique) (1987-1988): 1-11. <http://eudml.org/doc/111955>.

@article{Hislop1987-1988,
author = {Hislop, P. D.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {spectral theory; non compact manifolds; Laplace-Beltrami operator},
language = {eng},
pages = {1-11},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Spectral analysis of non-compact manifolds using commutator methods},
url = {http://eudml.org/doc/111955},
year = {1987-1988},
}

TY - JOUR
AU - Hislop, P. D.
TI - Spectral analysis of non-compact manifolds using commutator methods
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1987-1988
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 11
LA - eng
KW - spectral theory; non compact manifolds; Laplace-Beltrami operator
UR - http://eudml.org/doc/111955
ER -

References

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  1. [1] R.G. Froese, P.D. Hislop, Spectral Analysis of Second-Order Elliptic Operators on Non-compact Manifolds, to appear in Duke Mathematical Journal (1988) . Zbl0687.35060
  2. [2] I. Chavel, Eigenvalues in Riemannian Geometry. New York: Academic Press1984. Zbl0551.53001MR768584
  3. [3] J. Cheeger, D. Ebin, Comparison Theorems in Riemannian Geometry. Amsterdam: North Holland Publishing Co.1975. Zbl0309.53035MR458335
  4. [4] E. Mourre, Absence of Singular Continuous Spectrum for certain selfadjoint Operators. Commun. Math. Phys.78, 391-408 (1981). Zbl0489.47010MR603501
  5. [5] A. Selberg, Harmonic Analysis and Discontinuous Groups in Weakly Symmetric Riemmannian Spaces with Applications to Dirichlet Series. J. Ind. Math. Soc.20, 47-87 (1956). Zbl0072.08201MR88511
  6. [6] P. Lax, R.S. Phillips, Translation Representation for Automorphic Solutions of the non-Euclidean Wave Equation I, II, III. C.P.A.M.37, 303-328 (1984); 37, 779-813 (1984); 38, 179-208 (1985). Zbl0549.10019MR762873
  7. [7] S.J. Patterson, The Laplacian Operator on a Riemann Surface I, II, III. Compositio Math.31, 83-107 (1975); 32, 71-112 (1976); 33, 227-259 (1976). Zbl0342.30011MR384702
  8. [8] P.A. Perry, The Laplace Operator on a Hyperbolic Manifold I. Spectral and Scattering Theory. J. Funct. Anal.75161-182 (1987) (1988). Zbl0631.58030MR911204
  9. [9] S. Agmon, Spectral Theory of Schrödinger Operators on Euclidean and non-Euclidean Spaces. C.P.A.M.39,par.3 par.16, Number S, Supplement (1986). Zbl0601.47039MR861480
  10. [10] R. Mazzeo, R. Melrose, Meromorphic Extension of the Resolvent on Complete spaces with Asymptotically Constant Negative Curvature. J. Funct. Anal.75, 260-310 (1987). Zbl0636.58034MR916753
  11. [11] H.L. Cyon, R.G. Froese, W. Kirsch, B. Simon, Schrödinger Operators, with Application to Quantum Mechanics and Global Geometry. Berlin: Springer-Verlag1987. Zbl0619.47005MR883643
  12. [12] R.G. Froese, P.D. Hislop, Analysis of the Point Spectrum of Second Order Elliptic Operators on Non-compact Manifolds, preprint (1988). Zbl0687.35060
  13. [13] S. Debievre, P.D. Hislop, Scattering Theory for the Wave and Schrödinger Equations on Non-compact Manifolds, preprint (1988). Zbl0778.58064
  14. [14] R. Froese, I. Herbst, Exponential Bounds and Absence of positive Eigenvalues for N-Body Schrödinger Operators. Commun. Math. Phys.87, 429-447 (1982). Zbl0509.35061MR682117
  15. [15] P. Lax, R.S. Phillips, Scattering Theory for Automorphic Functions. Annals of Mathematics Studies87. Princeton: Princeton University Press1976. Zbl0362.10022MR562288
  16. [16] Y. Colin De Verdiere, Pseudo-Laplacians II. Ann. Inst. Fourier33, 87-113 (1983). Zbl0496.58016MR699488

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