Variation de la phase de diffusion et distribution des résonances
Vesselin Petkov[1]; Maciej Zworski[2]
- [1] Département de Mathématiques Appliquées, Université de Bordeaux I, 351, Cours de la Libération, 33405 Talence, FRANCE
- [2] Mathematics Department, University of California, Evans Hall, Berkeley, CA 94720, USA
Séminaire Équations aux dérivées partielles (1998-1999)
- Volume: 1998-1999, page 1-12
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topPetkov, Vesselin, and Zworski, Maciej. "Variation de la phase de diffusion et distribution des résonances." Séminaire Équations aux dérivées partielles 1998-1999 (1998-1999): 1-12. <http://eudml.org/doc/10962>.
@article{Petkov1998-1999,
affiliation = {Département de Mathématiques Appliquées, Université de Bordeaux I, 351, Cours de la Libération, 33405 Talence, FRANCE; Mathematics Department, University of California, Evans Hall, Berkeley, CA 94720, USA},
author = {Petkov, Vesselin, Zworski, Maciej},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {Laplacian perturbations; Breit-Wigner formulas; scattering poles; spectral asymptotics; Weyl asymptotics},
language = {fre},
pages = {1-12},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Variation de la phase de diffusion et distribution des résonances},
url = {http://eudml.org/doc/10962},
volume = {1998-1999},
year = {1998-1999},
}
TY - JOUR
AU - Petkov, Vesselin
AU - Zworski, Maciej
TI - Variation de la phase de diffusion et distribution des résonances
JO - Séminaire Équations aux dérivées partielles
PY - 1998-1999
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1998-1999
SP - 1
EP - 12
LA - fre
KW - Laplacian perturbations; Breit-Wigner formulas; scattering poles; spectral asymptotics; Weyl asymptotics
UR - http://eudml.org/doc/10962
ER -
References
top- N. Burq Décroissance de l’énergie locale de l’équation des ondes pour le problème extérieur et absence de résonance au voisinage du réel, Acta Math. 180 (1998), 1–29. Zbl0918.35081
- T. Christiansen, Spectral asymptotics for general compactly supported perturbations of the Laplacian on , Comm. P.D.E. 23(1998), 933-947. Zbl0912.35115MR1632784
- C.Gérard, A. Martinez and D. Robert, Breit-Wigner formulas for the scattering poles and total scattering cross-section in the semi-classical limit, Comm. Math. Phys. 121 (1989) 323-336. Zbl0704.35114MR985402
- L. Guillopé and M. Zworski, Scattering asymptotics for Riemann surfaces, Ann. of Math. 129(1997), 597-660. Zbl0898.58054MR1454705
- T.E.Guriev and Yu.S.Safarov, Precise asymptotics of the spectrum for the Laplace operator on manifolds with periodic geodesics, Trudy Matem. Inst. Steklov, 179 (1988) (in Russian) ; English translation in Proc. Steklov Institute of Mathematics, 179 (1989), 35-53. Zbl0701.58058
- W.K. Hayman, Subharmonic Functions, vol.II, Academic Press, London, 1989. Zbl0699.31001MR1049148
- L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. III, Springer-Verlag, Berlin, 1985. Zbl0601.35001
- R.B.Melrose, Polynomial bounds on the number of the 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 EDP, Saint-Jean-de-Monts, 1984. Zbl0621.35073
- R.B.Melrose, Weyl asymptotics for the phase in obstacle scattring, Comm. P.D.E., 13 (1988), 1431-1439. Zbl0686.35089MR956828
- V. Petkov, Weyl asymptotic of the scattering phase for metric perturbations, Asymptotic Analysis, 10 (1995), 245-261. Zbl0856.35097MR1332383
- V. Petkov and G. Vodev, Upper bounds on the number of scattering poles and the Lax-Phillips conjecture, Asymptotic Analysis, 7 (1993), 97-104. Zbl0801.35099MR1225440
- V. Petkov and M. Zworski, Breit-Wigner approximation and the distribution of resonances, Comm. Math. Physics, (to appear). Zbl0936.47004MR1704278
- G. Popov, On the contribution of degenerate periodic trajectories to the wave trace, Comm. Math. Physics, 196 (1998), 363-383. Zbl0924.58100MR1645007
- D. Robert, Asymptotique de la phase de diffusion à haute énergie pour des perturbations du seconde ordre du Laplacien, Ann. Sci. Ecole Norm.Sup. Sér. 25 (1992), 107-134. Zbl0801.35100MR1169349
- D. Robert, Relative time-delay for perturbations of elliptic operators and semiclassical asymptotics, J. Funct. Anal. 126 (1994), 36-82. Zbl0813.35073MR1305063
- Yu. Safarov, Asymptotics of the spectrum of pseudodifferential operators with periodic characteristics, Zap. Nauchn. sem. Leningrad. Otdel Mat. Inst. Steklov, 152 (1986), 94-104 (in Russian) ; English translation in J. Soviet Math. 40 (1988), 645-652. Zbl0621.35071MR869246
- Yu. Safarov and D. Vassiliev, Branching Hamiltonian billiards, Dokl. AN SSSR, 301 (1988), 271-274 ; English tranlsation in Sov. Math. Dokl. 38 (1989), 64-68. Zbl0671.58012MR967818
- Yu. Safarov and D. Vassiliev, The asymptotic distribution of eigenvalues of partial differential equations, Translations of mathematical monographs, AMS, vol. 155, 1996. Zbl0870.35003
- J. Sjöstrand, A trace formula and review of some estimates for resonances, in Microlocal analysis and spectral theory (Lucca, 1996), 377–437, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 490, Kluwer Acad. Publ., Dordrecht, 1997. Zbl0877.35090MR1451399
- 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, Comm. P.D.E., 18 (1993), 847-857. Zbl0784.35070MR1218521
- J. Sjöstrand and M. Zworski. Lower bounds on the number of scattering poles, II, J. Funct. Anal. 123 (1994), 336-367. Zbl0823.35137MR1283032
- P. Stefanov, Quasimodes and resonances : fine lower bounds, to appear in Duke Math. J. Zbl0952.47013MR1700740
- E.C.Titchmarsh, The Theory of Functions, Oxford University, Oxford, 1968. Zbl0005.21004
- G. Vodev, Sharp bounds on the number of scattering poles for perturbations of the Laplacian, Comm. Math. Phys. 146 (1992), 205-216. Zbl0766.35032MR1163673
- G. Vodev, On the distribution of scattering poles for perturbations of the Laplacian, Ann. Inst. Fourier (Grenoble) 42 (1992), 625-635. Zbl0738.35054MR1182642
- G. Vodev, Sharp bounds on the number of scattering poles in even-dimensional spaces, Duke Math. J. 74 (1994), 1-17. Zbl0813.35075MR1271461
- G. Vodev, Sharp bounds on the number of scattering poles in two dimensional case, Math. Nachr. 170 (1994), 287-297. Zbl0829.35091MR1302380
- M. Zworski, Distribution of poles for scattering on the real line,J. Funct. Anal. 73 (1987), 277–296. Zbl0662.34033MR899652
- M. Zworski, Sharp polynomial bounds on the number of scattering poles, Duke Math. J. 59 (1989), 311-323. Zbl0705.35099MR1016891
- M. Zworski, Poisson formulae for resonaces, Séminaire E.D.P., Ecole Polytechnique, Exposé XIII, 1996-1997. Zbl1255.35084MR1482819
- M. Zworski, Poisson formula for resonances in even dimensions. Asian J. Math. 2 (1998), 615-624. Zbl0932.47004MR1724627
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