Free Access
Volume 41, Number 5, September-October 2007
Page(s) 925 - 943
Published online 23 October 2007
  1. M. Abramowitz and I.A. Stegun, Handbook of mathematical functions. Dover Publications, New York, 9th edn. (1970).
  2. J. Aguilar and J.M. Combes, A class of analytic perturbations for one-body Schrödinger hamiltonians. Comm. Math. Phys. 22 (1971) 269–279. [CrossRef] [MathSciNet]
  3. C. Alves and T. Ha Duong, Numerical experiments on the resonance poles associated to acoustic and elastic scattering by a plane crack, in Mathematical and Numerical Aspects of Wave Propagation, E. Bécache et al. Eds., SIAM (1995).
  4. C. Amrouche, The Neumann problem in the half-space. C. R. Acad. Sci. Paris Ser. I 335 (2002) 151–156.
  5. A. Bachelot and A. Motet-Bachelot, Les résonances d'un trou noir de Schwarzschild. Ann. Henri. Poincarré 59 (1993) 280–294.
  6. E. Balslev and J.M. Combes, Spectral properties of many body Schrödinger operators with dilation analytic interactions. Comm. Math. Phys. 22 (1971) 280–294. [CrossRef] [MathSciNet]
  7. C.E. Baum, The Singularity Expansion Method, in Transient Electromagnetic Fields, L.B. Felsen Ed., Springer-Verlag, New York (1976).
  8. H. Brezis, Analyse fonctionnelle, Théorie et application. Masson, Paris (1983).
  9. N. Burq and M. Zworski, Resonance expansions in semi-classical propagation. Comm. Math. Phys. 232 (2001) 1–12. [CrossRef]
  10. M.P. Carpentier and A.F. Dos Santos, Solution of equations involving analytic functions. J. Comput. Phys. 45 (1982) 210–220. [CrossRef] [MathSciNet]
  11. P.G. Ciarlet and P. Destuynder, A justification of the two-dimensional linear plate model. J. Mécanique 18 (1979) 315–344.
  12. R. Dautray and J.L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Tome 1, Dunod, Paris (1984).
  13. R. Dautray and J.L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Tome 3, Dunod, Paris (1985).
  14. L.B. Felsen and E. Heyman, Hybrid ray mode analysis of transient scattering, in Low and Frequency Asymptotics, V.K. Varadan and V.V. Varadan Eds. (1986).
  15. D. Habault and P.J.T. Filippi, Light fluid approximation for sound radiation and diffraction by thin elastic plates. J. Sound Vibration 213 (1998) 333–374. [CrossRef]
  16. C. Hazard, The Singularity Expansion Method, in Fifth International Conference on Mathematical and Numerical Aspects of Wave propagation, SIAM (2000) 494–498.
  17. C. Hazard and M. Lenoir, Determination of scattering frequencies for an elastic floating body. SIAM J. Math. Anal. 24 (1993) 1458–1514. [CrossRef] [MathSciNet]
  18. C. Hazard and F. Loret, Generalized eigenfunction expansions for conservative scattering problems with an application to water waves. Proceedings of the Royal Society of Edinburgh (2007) Accepted.
  19. T. Kato, Perturbation theory for linear operators. Springer-Verlag, New York (1984).
  20. F. Klopp and M. Zworski, Generic simplicity of resonances. Helv. Phys. Acta 8 (1995) 531–538.
  21. K. Knopp, Theory of functions, Part II. Dover, New York (1947).
  22. P. Kravanja and M. Van Barel, Computing the zeros of analytic functions. Lect. Notes Math. 1727, Springer (2000).
  23. N. Kuznetsov, V. Maz'ya and B. Vainberg, Linear Water Waves, a Mathematical Approach. Cambridge (2002).
  24. C. Labreuche, Problèmes inverses en diffraction d'ondes basés sur la notion de résonances. Ph.D. thesis, University of Paris IX, France (1997).
  25. P.D. Lax and R.S. Phillips, Decaying modes for the wave equation in the exterior of an obstacle. Comm. Pure Appl. Math. 22 (1969) 737–787. [CrossRef] [MathSciNet]
  26. M. Lenoir, M. Vullierme-Ledard and C. Hazard, Variational formulations for the determination of resonant states in scattering problems. SIAM J. Math. Anal. 23 (1992) 579–608. [CrossRef] [MathSciNet]
  27. T.-Y. Li, On locating all zeros of an analytic function within a bounded domain by a revised Delvess/Lyness method. SIAM J. Numer. Anal. 20 (1983).
  28. F. Loret, Time-harmonic or resonant states decomposition for the simulation of the time-dependent solution of a sea-keeping problem. Ph.D. thesis, Centrale Paris school, France (2004).
  29. G. Majda, W. Strauss and M. Wei, Numerical computation of the scattering frequencies for acoustic wave equations. Comput. Phys. 75 (1988) 345–358. [CrossRef]
  30. S.J. Maskell and F. Ursell, The transient motion of a floating body. J. Fluid Mech 44 (1970) 303–313. [CrossRef]
  31. C. Maury and P.J.T. Filippi, Transient acoustic diffraction and radiation by an axisymmetrical elastic shell: a new statement of the basic equations and a numerical method based on polynomial approximations. J. Sound Vibration 241 (2001) 459–483. [CrossRef]
  32. M.H. Meylan, Spectral solution of time dependent shallow water hydroelasticity. J. Fluid Mech. 454 (2002) 387–402. [CrossRef]
  33. L.W. Pearson, D.R. Wilton and R. Mittra, Some implications of the Laplace transform inversion on SEM coupling coefficients in the time domain, in Electromagnetics, Hemisphere Publisher, Washington DC 2 (1982) 181–200.
  34. O. Poisson, Étude numérique des pôles de résonance associés à la diffraction d'ondes acoustiques et élastiques par un obstacle en dimension 2. RAIRO Modèle. Anal. Numér. 29 (1995) 819–855.
  35. R.J. Prony, L'École Polytechnique (Paris), 1, cahier 2, 24 (1795).
  36. T.K. Sarkar, S. Park, J. Koh and S. Rao, Application of the matrix pencil method for estimating the SEM (Singularity Expansion Method) poles of source-free transient responses from multiple look directions. IEEE Trans. Antennas Propagation 48 (2000) 612–618. [CrossRef]
  37. R.H. Schafer and R.G. Kouyoumjian, Transient currents on a cylinder illuminated by an impulsive plane wave. IEEE Trans. Antennas Propagation ap-23 (1975) 627–638.
  38. S. Steinberg, Meromorphic families of compact operators. Arch. Rational Mech. Anal. 31 (1968) 372–380. [CrossRef] [MathSciNet]
  39. S.H. Tang and M. Zworski, Resonance expansions of scattered waves. Comm. Pure Appl. Math. 53 (2000) 1305–1334. [CrossRef] [MathSciNet]
  40. A.G. Tijhuis and R.M. van der Weiden, SEM approach to transient scattering by a lossy, radially inhomogeneous dielectric circular cylinder. Wave Motion 8 (1986) 43–63. [CrossRef] [MathSciNet]
  41. H. Überall and G.C. Gaunard, The physical content of the singularity expansion method. Appl. Plys. Lett. 39 (1981) 362–364. [CrossRef]
  42. B.R. Vainberg, Asymptotic methods in equations of mathematical physics. Gordon and Breach Science Publishers (1989).
  43. J.V. Wehausen and E.V. Laitone, Surface waves, in Hanbuch der Physik IX, Springer-Verlag, Berlin (1960).

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you