Classical and quantum resonances for hyperbolic surfaces

作者: Colin Guillarmou , Joachim Hilgert , Tobias Weich

DOI: 10.1007/S00208-017-1576-5

关键词:

摘要: For compact and for convex co-compact oriented hyperbolic surfaces, we prove an explicit correspondence between classical Ruelle resonant states quantum states, except at negative integers where the involves holomorphic sections of line bundles.

参考文章(37)
H. Schlichtkrull, E. P. Van Den Ban, Asymptotic expansions and boundary values of eigenfunctions on Riemannian symmetric spaces Crelle's Journal. ,vol. 380, pp. 108- 165 ,(1987)
Otto Forster, Lectures on Riemann surfaces Springer New York. ,(1981) , 10.1007/978-1-4612-5961-9
S. J. Patterson, The limit set of a Fuchsian group Acta Mathematica. ,vol. 136, pp. 241- 273 ,(1976) , 10.1007/BF02392046
Rafe R Mazzeo, Richard B Melrose, Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature Journal of Functional Analysis. ,vol. 75, pp. 260- 310 ,(1987) , 10.1016/0022-1236(87)90097-8
Frédéric Faure, Johannes Sjöstrand, Upper bound on the density of Ruelle resonances for Anosov flows arXiv: Mathematical Physics. ,(2010) , 10.1007/S00220-011-1349-Z
Rafe Mazzeo, Unique Continuation at Infinity and Embedded Eigenvalues for Asymptotically Hyperbolic Manifolds American Journal of Mathematics. ,vol. 113, pp. 25- ,(1991) , 10.2307/2374820
C. Guillarmou, J. Qing, Spectral Characterization of Poincaré–Einstein Manifolds with Infinity of Positive Yamabe Type International Mathematics Research Notices. ,vol. 2010, pp. 1720- 1740 ,(2009) , 10.1093/IMRN/RNP188
Laurent Guillope, Maciej Zworski, Scattering asymptotics for Riemann surfaces Annals of Mathematics. ,vol. 145, pp. 597- 660 ,(1997) , 10.2307/2951846
V. Guillemin, D. Kazhdan, Some inverse spectral results for negatively curved 2-manifolds Topology. ,vol. 19, pp. 301- 312 ,(1980) , 10.1016/0040-9383(80)90015-4