Polynomial bounds on the number of resonances for some complete spaces of constant negative curvature near infinity
作者： Laurent Guillopé , Maciej Zworski
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摘要: Guillope,L. and M. Zworski, Polynomial bounds on the number of resonances for some complete spaces constant negative curvature near infinity, Asymptotic Analysis 11 (1995) 1-22. Let X be a conforrnally compact n-dimensional manifold with -1 infinity. The resolvent (ilsCn 1 s»-I, Re s > n 1, Laplacian extends to meromorphic family operators C its poles are called or scattering poles. If NxCr) is in disc radius r we prove following upper bound: :( Crn+! + C.
sci-hub.se 参考文章(18)
The Laplace operator on a hyperbolic manifold. II. Eisenstein series and the scattering matrix. Crelle's Journal. ,vol. 1989, pp. 67- 91 ,(1989) , 10.1515/CRLL.1989.398.67
Richard B. Melrose, The Atiyah-Patodi-Singer Index Theorem ,(1993)
Lars Hörmander, The analysis of linear partial differential operators Springer-Verlag. ,(1990)
S.J. PATTERSON, The Selberg Zeta-Function of a Kleinian Group Number Theory, Trace Formulas and Discrete Groups#R##N#Symposium in Honor of Atle Selberg, Oslo, Norway, July 14–21, 1987. pp. 409- 441 ,(1989) , 10.1016/B978-0-12-067570-8.50031-7
Peter A. Perry, The Selberg zeta function and a local trace formula for Kleinian groups. Crelle's Journal. ,vol. 410, pp. 116- 152 ,(1990)
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
Georgi Vodev, Sharp polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in ? n Mathematische Annalen. ,vol. 291, pp. 39- 49 ,(1991) , 10.1007/BF01445189
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
Peter A. Perry, The Selberg zeta function and scattering poles for Kleinian groups Bulletin of the American Mathematical Society. ,vol. 24, pp. 327- 333 ,(1991) , 10.1090/S0273-0979-1991-16024-6
Maciej Zworski, Sharp polynomial bounds on the number of scattering poles Duke Mathematical Journal. ,vol. 59, pp. 311- 323 ,(1989) , 10.1215/S0012-7094-89-05913-9