Variation de la phase de diffusion et distribution des résonances

Petkov, Vesselin; Zworski, Maciej

Petkov, Vesselin ¹ ; Zworski, Maciej 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 (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 12, 12 p.

MR Zbl

Affiliations des auteurs :

Petkov, Vesselin ¹ ; Zworski, Maciej ²

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     pages = {1--12},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {1998-1999},
     zbl = {1061.35505},
     mrnumber = {1721330},
     language = {fr},
     url = {http://archive.numdam.org/item/SEDP_1998-1999____A12_0/}
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Petkov, Vesselin; Zworski, Maciej. Variation de la phase de diffusion et distribution des résonances. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 12, 12 p. http://archive.numdam.org/item/SEDP_1998-1999____A12_0/

Bibliographie
Cité par

[1] 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. | Zbl

[2] T. Christiansen, Spectral asymptotics for general compactly supported perturbations of the Laplacian on $ℝ^{n}$ , Comm. P.D.E. 23(1998), 933-947. | MR | Zbl

[3] 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. | MR | Zbl

[4] L. Guillopé and M. Zworski, Scattering asymptotics for Riemann surfaces, Ann. of Math. 129(1997), 597-660. | MR | Zbl

[5] 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. | Zbl

[6] W.K. Hayman, Subharmonic Functions, vol.II, Academic Press, London, 1989. | MR | Zbl

[7] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. III, Springer-Verlag, Berlin, 1985. | Zbl

[8] R.B.Melrose, Polynomial bounds on the number of the scattering poles, J. Funct. Anal.,53 (1983), 287-303. | MR | Zbl

[9] R.B.Melrose, Polynomial bounds on the distribution of poles in scattering by an obstacle, Journées EDP, Saint-Jean-de-Monts, 1984. | Numdam | Zbl

[10] R.B.Melrose, Weyl asymptotics for the phase in obstacle scattring, Comm. P.D.E., 13 (1988), 1431-1439. | MR | Zbl

[11] V. Petkov, Weyl asymptotic of the scattering phase for metric perturbations, Asymptotic Analysis, 10 (1995), 245-261. | MR | Zbl

[12] V. Petkov and G. Vodev, Upper bounds on the number of scattering poles and the Lax-Phillips conjecture, Asymptotic Analysis, 7 (1993), 97-104. | MR | Zbl

[13] V. Petkov and M. Zworski, Breit-Wigner approximation and the distribution of resonances, Comm. Math. Physics, (to appear). | MR | Zbl

[14] G. Popov, On the contribution of degenerate periodic trajectories to the wave trace, Comm. Math. Physics, 196 (1998), 363-383. | MR | Zbl

[15] 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. | Numdam | MR | Zbl

[16] D. Robert, Relative time-delay for perturbations of elliptic operators and semiclassical asymptotics, J. Funct. Anal. 126 (1994), 36-82. | MR | Zbl

[17] 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. | MR | Zbl

[18] 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. | MR | Zbl

[19] Yu. Safarov and D. Vassiliev, The asymptotic distribution of eigenvalues of partial differential equations, Translations of mathematical monographs, AMS, vol. 155, 1996. | Zbl

[20] 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. | MR | Zbl

[21] J. Sjöstrand and M. Zworski, Complex scaling and the distribution of scattering poles, J. Amer. Math. Soc. 4 (1991), 729-769. | MR | Zbl

[22] J. Sjöstrand and M. Zworski. Lower bounds on the number of scattering poles, Comm. P.D.E., 18 (1993), 847-857. | MR | Zbl

[23] J. Sjöstrand and M. Zworski. Lower bounds on the number of scattering poles, II, J. Funct. Anal. 123 (1994), 336-367. | MR | Zbl

[24] P. Stefanov, Quasimodes and resonances : fine lower bounds, to appear in Duke Math. J. | MR | Zbl

[25] E.C.Titchmarsh, The Theory of Functions, Oxford University, Oxford, 1968.

[26] G. Vodev, Sharp bounds on the number of scattering poles for perturbations of the Laplacian, Comm. Math. Phys. 146 (1992), 205-216. | MR | Zbl

[27] G. Vodev, On the distribution of scattering poles for perturbations of the Laplacian, Ann. Inst. Fourier (Grenoble) 42 (1992), 625-635. | Numdam | MR | Zbl

[28] G. Vodev, Sharp bounds on the number of scattering poles in even-dimensional spaces, Duke Math. J. 74 (1994), 1-17. | MR | Zbl

[29] G. Vodev, Sharp bounds on the number of scattering poles in two dimensional case, Math. Nachr. 170 (1994), 287-297. | MR | Zbl

[30] M. Zworski, Distribution of poles for scattering on the real line,J. Funct. Anal. 73 (1987), 277–296. | MR | Zbl

[31] M. Zworski, Sharp polynomial bounds on the number of scattering poles, Duke Math. J. 59 (1989), 311-323. | MR | Zbl

[32] M. Zworski, Poisson formulae for resonaces, Séminaire E.D.P., Ecole Polytechnique, Exposé XIII, 1996-1997. | Numdam | MR | Zbl

[33] M. Zworski, Poisson formula for resonances in even dimensions. Asian J. Math. 2 (1998), 615-624. | MR | Zbl