Spectral resonances for the Laplace-Beltrami operator
Stephen De Bièvre; Peter D. Hislop
Annales de l'I.H.P. Physique théorique (1988)
- Volume: 48, Issue: 2, page 105-145
- ISSN: 0246-0211
Access Full Article
topHow to cite
topDe Bièvre, Stephen, and Hislop, Peter D.. "Spectral resonances for the Laplace-Beltrami operator." Annales de l'I.H.P. Physique théorique 48.2 (1988): 105-145. <http://eudml.org/doc/76392>.
@article{DeBièvre1988,
author = {De Bièvre, Stephen, Hislop, Peter D.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {spectral theory; Laplace-Beltrami operator; Riemannian manifolds; spectral resonances},
language = {eng},
number = {2},
pages = {105-145},
publisher = {Gauthier-Villars},
title = {Spectral resonances for the Laplace-Beltrami operator},
url = {http://eudml.org/doc/76392},
volume = {48},
year = {1988},
}
TY - JOUR
AU - De Bièvre, Stephen
AU - Hislop, Peter D.
TI - Spectral resonances for the Laplace-Beltrami operator
JO - Annales de l'I.H.P. Physique théorique
PY - 1988
PB - Gauthier-Villars
VL - 48
IS - 2
SP - 105
EP - 145
LA - eng
KW - spectral theory; Laplace-Beltrami operator; Riemannian manifolds; spectral resonances
UR - http://eudml.org/doc/76392
ER -
References
top- [1] P.D. Hislop, I.M. Sigal, Shape Resonances in Quantum Mechanics. University of California, Irvine preprint 1986, to be published in Memoirs of the American Mathematical Society. MR921268
- [2] J.-M. Combes, P. Duclos, M. Klein, R. Seiler, The Shape Resonance. Commun. Math. Phys., t. 110, 1987, p. 215-216. Zbl0629.47044MR887996
- [3] B. Helffer, Sjöstrand, Resonances en Limite Semi-Classique. Mémoire de la Société Mathématique de France, no. 24/25, Supplément au Bulletin de la S. M. F., t. 114, 1986. Zbl0631.35075
- [4] S. Graffi, K. Yajima, Exterior scaling and the AC-Stark effect in a Coulomb field. Commun. Math. Phys., t. 89, 1983, p. 277-301. Zbl0522.35085MR709468
- [5] I. Herbst, Dilation Analyticity in constant electric field, I. The two-body problem. Commun. Math. Phys., t. 64, 1979, p. 279-298. Zbl0447.47028MR520094
- [6] J.E. Avron, I. Herbst, B. Simon, Schrödinger Operators with magnetic fields III. Atoms in homogeneous magnetic fields. Commun. Math. Phys., t. 79, 1981, p. 529-572. Zbl0464.35086MR623966
- [7] J.F. Escobar, On the spectrum of the Laplacian on complete Riemannian manifolds. Comm. in Partial Differential Equations, t. 11 (1), 1986, p. 63-85. Zbl0585.58046MR814547
- [8] R.G. Froese, P.D. Hislop, Analysis of Point Spectrum of Second Order Elliptic Operators on Non-compact Manifolds. CPTMarseille preprint 1988.
- [9] Ph Briet, J.M. Combes, P. Duclos, On the location of Resonances for Schrödinger Operators in the semiclassical limit. III. Shape Resonances. CPTMarseille preprint, 1987 ; Sigal, I. M.: Exponential Bounds on Resonance States and Width of Resonances. University of Toronto preprint, 1987. Zbl0629.47043
- [10] R. Abraham, J.E. Marsden, Foundations of Mechanics. London: Benjamin Cummings Publishing Co., 1978. Zbl0393.70001MR515141
- [11] P. Chernoff, Essential Self-Adjointness of powers of generators of hyperbolic equations. J. Functional Analysis, t. 12, 1972, p. 401-414. Zbl0263.35066MR369890
- [12] M. Spivak, A Comprehensive Introduction to Differential Geometry. I. Delaware: Publish or Perish, Inc. 1970.
- [13] M. Reed, B. Simon, Methods of Modern Mathematical Physics, II. Fourier Analysis, Self-Adjointness. New York: Academic Press1975. Zbl0308.47002MR493420
- [14] M. Reed, B. Simon, Methods of Modern Mathematical Physics, IV. Analysis of Operators. New York: Academic Press, 1978. Zbl0401.47001MR493421
- [15] S.T. Yau, Some function theoretic properties of complete Riemannian manifolds and their applications to geometry. Indiana Univ. Math. J., t. 25, 1976, p. 659-670. Zbl0335.53041MR417452
- [16] B. Simon, Semiclassical Analysis of Low Lying Eigenvalues I. Nondegenerate Minima: Asymptotic Expansions. Ann. Inst. Henri Poincaré, t. 13, 1983, p. 296-307. Zbl0526.35027MR708966
- [17] Ph Briet, J.M. Combes, P. Duclos, On the Location of Resonances for Schrödinger Operators in the semiclassical limit. I : Resonance free domains. J. Math. Analy. and Appl., t. 126, 1987, p. 90-99. Zbl0629.47043MR900530
- [18] S. Agmon, Lectures on exponential decay of solutions of second-order elliptic equations. Princeton: Princeton University Press, 1982. Zbl0503.35001MR745286
- [19] B. Simon, Semiclassical Analysis of Low Lying Eigenvalues II. Tunneling. Ann. Math., t. 120, 1984, p. 89-118. Zbl0626.35070MR750717
- [20] L.P. Horwitz, I.M. Sigal, On a mathematical model for non-stationary physical systems. Helv. Phys. Acta, t. 51, 1978, p. 685-715. MR542800
- [21] P. Deift, W. Hunziker, B. Simon, E. Vock, Pointwise Bounds on Eigenfunctions and Wave Packets in N-Body Quantum Systems IV. Commun. Math. Phys., t. 64, 1978, p. 1-34. Zbl0419.35079MR516993
- [22] B.S. Dewitt, Dynamical Theory in Curved Spaces I. A Review of the Classical and Quantum Action Principles. Rev. Mod. Phys., t. 29, 1957, p. 377-397. Zbl0118.23301MR95691
- [23] K.S. Cheng, Quantization of a General Dynamical System by Feynman's Path Integration Formulation. J. Math. Phys., t. 13, 1972, p. 1723-1726.
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.