Resonance expansions in wave propagation

Maciej Zworski[1]

  • [1] Department of Mathematics, University of California, Berkeley

Séminaire Équations aux dérivées partielles (1999-2000)

  • Volume: 1999-2000, page 1-9

How to cite


Zworski, Maciej. "Resonance expansions in wave propagation." Séminaire Équations aux dérivées partielles 1999-2000 (1999-2000): 1-9. <>.

affiliation = {Department of Mathematics, University of California, Berkeley},
author = {Zworski, Maciej},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-9},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Resonance expansions in wave propagation},
url = {},
volume = {1999-2000},
year = {1999-2000},

AU - Zworski, Maciej
TI - Resonance expansions in wave propagation
JO - Séminaire Équations aux dérivées partielles
PY - 1999-2000
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1999-2000
SP - 1
EP - 9
LA - eng
UR -
ER -


  1. Bardos, C., Guillot, J.-C., and Ralston, J., La relation de Poisson pour l’équation des ondes dans un ouvert non borné, Comm. P.D.E. 7(1982), 905-958. Zbl0496.35067
  2. Burq, N., and Zworski, M., Resonance expansions in semi-classical propagation, preprint, 2000. Zbl1042.81582MR1860756
  3. Christiansen, T. and Zworski, M., Resonance wave expansions: two hyperbolic examples, preprint, 1999, to appear in Comm. Math. Phys. Zbl0955.58024MR1772249
  4. Dimassi, M. and Sjöstrand, J., Spectral asymptotics in the semi-classical limit, LMS Lecture Series, Cambridge University Press, 1999. Zbl0926.35002MR1735654
  5. Gérard, C., Martinez, A., and Robert, D., 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
  6. L. Guillopé and M. Zworski, Scattering asymptotics for Riemann surfaces. Ann. Math. 145 (1997), 597-660. Zbl0898.58054MR1454705
  7. Lax, P. and Phillips, R., Scattering Theory, Academic Press, 1969, 2nd edition 1989. Zbl0186.16301MR1037774
  8. Majda, G., Strauss, W., and Wei, M. Numerical computation of the scattering frequencies for acoustic wave equations. J. Comp. Physics 75 (1988), 345-358. Zbl0643.65080
  9. Mandelshtam, V.A., and Taylor, H.S., Harmonic inversion of time signals and its applications, J. Chem. Phys. 107(1997), 6756-6769. 
  10. Melrose, R. B. Singularities and energy decay in acoustical scattering. Duke Math. J. 46 (1979), no. 1, 43-59. Zbl0415.35050MR523601
  11. Melrose, R. B. Polynomial bound on the number of scattering poles. J. Funct. Anal.53 (1983), no. 3, 287–303. Zbl0535.35067MR724031
  12. Merkli, M., Sigal, I. M. A time-dependent theory of quantum resonances. Comm. Math. Phys. 201 (1999), 549–576. Zbl0934.47007MR1685889
  13. Miller, W.H., Tunneling and state specificity in unimolecular reactions, Chem. Rev. 87(1987), 19-27. 
  14. Morawetz, C.S. Decay of solutions of the exterior problems for the wave equation. Comm. Pure Appl. Math. 14 (1961), 561-568. Zbl0101.07701MR132908
  15. Peskin, U., Reisler, H., and Miller, W. H. On the relation between unimolegular reaction rates and overlapping resonances. J. Chem. Phys. 101 (1994), no. 11, 9672-9680. 
  16. Petkov, V., and Zworski, M., Breit-Wigner approximation and the distribution of resonancs, Comm. Math. Phys. 204(1999), 329-351. Zbl0936.47004MR1704278
  17. Petkov, V., and Zworski, M., Correction to [16], preprint, April 2000. 
  18. Prony, R., J. l’Ecole Polytechnique (Paris), 1, cahier 2, 24 (1795). 
  19. Sjöstrand, J., 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
  20. Sjöstrand, J., Resonances for bottles and trace formulae, preprint, 1998, to appear in Math. Nachrichten. Zbl0979.35109MR1806367
  21. Sjöstrand, J., and Zworski, M., Complex scaling and the distribution of scattering poles, Journal of A.M.S., 4(4)(1991), 729-769 Zbl0752.35046MR1115789
  22. Sjöstrand, J., and Zworski, M. Lower bounds on the number of scattering poles. II. J. Func. Anal. 123(1994), no. 2, 336-367. Zbl0823.35137MR1283032
  23. Soffer, A. and Weinstein, M. Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations. Invent. Math. 136 (1999), 9–74. Zbl0910.35107MR1681113
  24. Stefanov, P., Resonance expansions and Rayleigh waves, preprint, 2000. Zbl0987.35097MR1825264
  25. Stefanov, P., Quasimodes and Resonances: sharp lower bounds. Duke Math. J. 99, (1999), no. 1. 75-92. Zbl0952.47013MR1700740
  26. Stefanov, P., and Vodev, G. Neumann Resonances in Linear Elasticity for an Arbitrary Body. Comm. Math. Phys. 176 (1996), no. 3, 645-659. Zbl0851.35032MR1376435
  27. Vainberg, B. R. Exterior elliptic problems that depend polynomially on the spectral parameter, and the asymptotic behavior for large values of the time of the solutions of nonstationary problems. (Russian) Mat. Sb. (N.S.) 92(134) (1973), 224–241. Zbl0294.35031MR346319
  28. Tang, S.H. and Zworski, M. From quasimodes to resonances, Math. Res. Lett., 5(1998), 261-272 Zbl0913.35101MR1637824
  29. Tang, S.H. and Zworski, M. Resonance expansions of scattered waves, preprint 1999, to appear in Comm. Pure Appl. Math. Zbl1032.35148MR1768812
  30. Zworski, M., Poisson formulæ for resonances, Séminaire E.D.P. 1996-1997, École Polytechnique, XIII-1-XIII-12. Zbl1255.35084MR1482819
  31. Zworski, M., Poisson formulæ for resonances in even dimensions. Asian J. Math. 2 (1998), no. 3, 615-624. Zbl0932.47004MR1724627
  32. Zworski, M., Resonances in physics and geometry. Notices Amer. Math. Soc. 46 (1999), 319–328. Zbl1177.58021MR1668841

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