Spectral resonances for the Laplace-Beltrami operator
De Bièvre, Stephen ; Hislop, Peter D.
Annales de l'I.H.P. Physique théorique, Tome 49 (1988), p. 105-145 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPA_1988__48_2_105_0,
     author = {De Bi\`evre, Stephan and Hislop, Peter D.},
     title = {Spectral resonances for the Laplace-Beltrami operator},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {49},
     year = {1988},
     pages = {105-145},
     mrnumber = {952658},
     zbl = {0645.58041},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1988__48_2_105_0}
}

De Bièvre, Stephen; Hislop, Peter D. Spectral resonances for the Laplace-Beltrami operator. Annales de l'I.H.P. Physique théorique, Tome 49 (1988) pp. 105-145. http://gdmltest.u-ga.fr/item/AIHPA_1988__48_2_105_0/

[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. | MR 921268

[2] J.-M. Combes, P. Duclos, M. Klein, R. Seiler, The Shape Resonance. Commun. Math. Phys., t. 110, 1987, p. 215-216. | MR 887996 | Zbl 0629.47044

[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. | Numdam | Zbl 0631.35075

[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. | MR 709468 | Zbl 0522.35085

[5] I. Herbst, Dilation Analyticity in constant electric field, I. The two-body problem. Commun. Math. Phys., t. 64, 1979, p. 279-298. | MR 520094 | Zbl 0447.47028

[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. | MR 623966 | Zbl 0464.35086

[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. | MR 814547 | Zbl 0585.58046

[8] R.G. Froese, P.D. Hislop, Analysis of Point Spectrum of Second Order Elliptic Operators on Non-compact Manifolds. CPT Marseille 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. CPT Marseille preprint, 1987 ; Sigal, I. M.: Exponential Bounds on Resonance States and Width of Resonances. University of Toronto preprint, 1987.

[10] R. Abraham, J.E. Marsden, Foundations of Mechanics. London: Benjamin Cummings Publishing Co., 1978. | MR 515141 | Zbl 0393.70001

[11] P. Chernoff, Essential Self-Adjointness of powers of generators of hyperbolic equations. J. Functional Analysis, t. 12, 1972, p. 401-414. | MR 369890 | Zbl 0263.35066

[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 Press 1975. | MR 493420 | Zbl 0308.47002

[14] M. Reed, B. Simon, Methods of Modern Mathematical Physics, IV. Analysis of Operators. New York: Academic Press, 1978. | MR 493421 | Zbl 0401.47001

[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. | MR 417452 | Zbl 0335.53041

[16] B. Simon, Semiclassical Analysis of Low Lying Eigenvalues I. Nondegenerate Minima: Asymptotic Expansions. Ann. Inst. Henri Poincaré, t. 13, 1983, p. 296-307. | Numdam | MR 708966 | Zbl 0526.35027

[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. | MR 900530 | Zbl 0629.47043

[18] S. Agmon, Lectures on exponential decay of solutions of second-order elliptic equations. Princeton: Princeton University Press, 1982. | MR 745286 | Zbl 0503.35001

[19] B. Simon, Semiclassical Analysis of Low Lying Eigenvalues II. Tunneling. Ann. Math., t. 120, 1984, p. 89-118. | MR 750717 | Zbl 0626.35070

[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. | MR 542800

[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. | MR 516993 | Zbl 0419.35079

[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. | MR 95691 | Zbl 0118.23301

[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.