Poisson formulæ for resonances.
- [1] Department of Mathematics, University of Toronto, and Centre de Mathématiques, École Polytechnique
Séminaire Équations aux dérivées partielles (1996-1997)
- Volume: 1996-1997, page 1-12
Access Full Article
topHow to cite
topZworski, Maciej. "Poisson formulæ for resonances.." Séminaire Équations aux dérivées partielles 1996-1997 (1996-1997): 1-12. <http://eudml.org/doc/10917>.
@article{Zworski1996-1997,
affiliation = {Department of Mathematics, University of Toronto, and Centre de Mathématiques, École Polytechnique},
author = {Zworski, Maciej},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-12},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Poisson formulæ for resonances.},
url = {http://eudml.org/doc/10917},
volume = {1996-1997},
year = {1996-1997},
}
TY - JOUR
AU - Zworski, Maciej
TI - Poisson formulæ for resonances.
JO - Séminaire Équations aux dérivées partielles
PY - 1996-1997
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1996-1997
SP - 1
EP - 12
LA - eng
UR - http://eudml.org/doc/10917
ER -
References
top- Sh. Agmon. A perturbation theory for resonances, Journées “Équations aux Dérivées partielles”, Saint-Jean de Monts, 1996. Zbl0902.47007
- R. Bañuelos and A. Sá Barreto. On the heat trace of Schrödinger operators, Comm. Partial Differ. Equations 20 (1995), 2153-2164. Zbl0843.35016MR1361734
- C. Bardos, J.-C. Guillot and J.V. Ralston. La relation de Poisson pour l’équation des ondes dans un ouvert non borné, Commun. Partial Differ. Equations 7 (1982), 905–958. Zbl0496.35067
- V. Buslaev. Scattering plane waves, spectral asymptotics and trace formulas in exterior problems, Dokl. Akad. Nauk SSSR, 197 (1971), 999–1002. Zbl0224.47023MR278108
- I. C. Gohberg and M. G. Krein. Introduction to the theory of linear nonselfadjoint operators, Translations of mathematical monographs 18, American Mathematical Society, Providence, 1969. Zbl0181.13504MR246142
- L. Guillopé. Asymptotique de la phase de diffusion pour l’opérateur de Schrödinger avec potentiel, C.R. Acad. Sci., Paris, Ser.I 293(1981), 601-603. Zbl0487.35073
- L. Guillopé and M. Zworski. Upper bounds on the number of resonances for non-compact Riemann surfaces, J. Funct. Anal. 129 (1995), 364–389. Zbl0841.58063MR1327183
- L. Guillopé and M. Zworski. Scattering asymptotics for Riemann surfaces, to appear in Ann. of Math. Zbl0898.58054MR1454705
- L. Hörmander. The analysis of linear partial differential operators II, Springer Verlag, Berlin, 1983. Zbl1062.35004MR705278
- F. Klopp and M. Zworski. Generic simplicity of resonances, Helv.Phys. Acta. 68(1995), 531–538. Zbl0844.47040MR1395259
- P. Lax and R. Phillips. Decaying modes for the wave equation in the exterior of an obstacle. Comm. Pure App. Math. 22 (1969), 737–787. Zbl0181.38201MR254432
- P. Lax and R. Phillips. The time delay operator and a related trace formula. in Topics in Functional Analysis. Advances in Math. Suppl. Studies 3 (1978), 197–295. Zbl0463.47006MR538021
- R.B. Melrose. Scattering theory and the trace of the wave group, J. Func. Anal. 45 (1982), 429–440. Zbl0525.47007MR645644
- R.B. Melrose. Polynomial bounds on the number of scattering poles, J. Funct. Anal. 53 (1983), 287–303. Zbl0535.35067MR724031
- R.B. Melrose. Polynomial bounds on the distribution of poles in scattering by an obstacle, Journées “Équations aux Dérivées partielles”, Saint-Jean de Monts, 1984. Zbl0621.35073
- R.B. Melrose. Weyl asymptotics for the phase in obstacle scattering, Commun. Partial Diff. Equations 13(1988), 1431-1439. Zbl0686.35089MR956828
- R.B. Melrose. Geometric scattering theory, Cambridge University Press, Cambridge, New York, Melbourne, 1995. Zbl0849.58071MR1350074
- R.B. Melrose and M. Zworski. Scattering metrics and geodesic flow at infinity, Invent. Math. 124(1996), 389–436. Zbl0855.58058MR1369423
- G. Perla-Menzala and T. Schonbek. Scattering frequencies for the wave equation with potential term, J. Funct. Anal. 55(1984), 297-322. Zbl0536.35060MR734801
- W. Müller. Spectral geometry and scattering theory for certain complete surfaces of finite volume, Invent. Math. 109 (1992), 265–305. Zbl0772.58063MR1172692
- A. Sá Barreto and Siu-Hung Tang. Existence of resonances in metric scattering, in preparation. Zbl0912.35117
- A. Sá Barreto and M. Zworski. Existence of resonances in three dimensions, Comm. Math. Phys. 173(2) (1995), 401–415. Zbl0835.35099MR1355631
- A. Sá Barreto and M. Zworski. Existence of resonances in potential scattering, Comm. Pure Appl. Math. 49(1996), 1271-1280. Zbl0877.35087MR1414586
- J. Sjöstrand. A trace formula and review of some estimates for resonances, Publications du Centre de Mathématiques de l’École Polytechnique No.1153, Octobre, 1996. Zbl0877.35090
- J. Sjöstrand. A trace formula for resonances and application to semi-classical Schrödinger operators, Séminaire EDP, École Polytechnique, Novembre, 1996. Zbl1061.35506MR1482808
- J. Sjöstrand and M. Zworski. Complex scaling and the distribution of scattering poles, J. Amer. Math. Soc. 4 (1991), 729–769. Zbl0752.35046MR1115789
- J. Sjöstrand and M. Zworski. Lower bounds on the number of scattering poles II, J. Funct. Anal. 123 (1994), 336–367. Zbl0823.35137MR1283032
- E. C. Titchmarsh, The theory of functions, Oxford University Press, 1939 Zbl0022.14602
- G. Vodev. Sharp polynomial bounds on the number of scattering poles for perturbations of the Laplacian, Comm. Math. Phys. 146 (1992), 39–49. Zbl0766.35032MR1163673
- G. Vodev. Asymptotics of scattering poles for degenerate perturbations of the Laplacian, J. Funct. Anal. 138 (1996), 295-310. Zbl0862.35082MR1395960
- M. Zworski. Sharp polynomial bounds on the number of scattering poles, Duke Math. J. 59 (1989), 311–323. Zbl0705.35099MR1016891
- M. Zworski. A remark on isopolar potentials, unpublished note. Zbl0988.34067MR1856251
- M. Zworski. Counting scattering poles., Proceedings of the Taniguchi International Workshop Spectral and scattering theory, M. Ikawa Ed., Marcel Dekker, New York, Basel, Hong Kong, 1994. Zbl0823.35139MR1291635
Citations in EuDML Documents
top- T. J. Christiansen, P. D. Hislop, Resonances for Schrödinger operators with compactly supported potentials
- Hart F. Smith, Maciej Zworski, [unknown]
- Maciej Zworski, Resonance expansions in wave propagation
- Vesselin Petkov, Maciej Zworski, Variation de la phase de diffusion et distribution des résonances
- Alain Bachelot, Wave Equation and Causality Violation
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.