Geodesic
Control theory and high energy eigenfunctions
Burq, Nicolas1  ; Zworski, Maciej2 
1 Université Paris Sud, Mathématiques, Bât 425, 91405 Orsay Cedex
2 Mathematics Department, University of California. Evans Hall, Berkeley, CA 94720, USA
Journées équations aux dérivées partielles (2004), article no. 13, 10 p.

Voir la notice de l'acte provenant de la source Numdam

DOI : 10.5802/jedp.13

Burq, Nicolas 1 ; Zworski, Maciej 2

1 Université Paris Sud, Mathématiques, Bât 425, 91405 Orsay Cedex
2 Mathematics Department, University of California. Evans Hall, Berkeley, CA 94720, USA 
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Burq, Nicolas; Zworski, Maciej. Control theory and high energy eigenfunctions. Journées équations aux dérivées partielles (2004), article  no. 13, 10 p. doi : 10.5802/jedp.13. http://geodesic.mathdoc.fr/articles/10.5802/jedp.13/

[1] A. Bäcker, R. Schubert, and P. Stifter. On the number of bouncing ball modes in billiards. J. Phys. A: Math. Gen. 30:6783-6795, 1997. | Zbl | MR

[2] C. Bardos, G. Lebeau and J. Rauch. Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. SIAM J. Control Optim. 30:1024–1065, 1992. | Zbl | MR

[3] E. Bogomolny, U. Gerland, and C. Schmit, Models of intermediate spectral statistics, Phys. Rev. E 59:1315-1318, 1999.

[4] N. Burq Control for Schrodinger equations on product manifolds Unpublished, 1992

[5] N. Burq. Semi-classical estimates for the resolvent in non trapping geometries. Int. Math. Res. Notices, 5:221–241, 2002. | Zbl | MR

[6] N. Burq and P. Gérard, Condition nécessaire et suffisante pour la contrôlabilité exacte des ondes, Comptes Rendus de L’Académie des Sciences, 749–752,t.325, Série I, 1996 | Zbl | MR

[7] N. Burq and M. Zworski. Geometric control in the presence of a black box. Jour. Amer. Math. Soc. , 17:443-471, 2004. | Zbl | MR

[8] N. Burq and M. Zworski. Bouncing ball modes and quantum chaos, to appear in SIAM Review, 2004. | Zbl | MR

[9] N. Burq and G.Lebeau, Mesures de défaut de compacité, application au système de Lamé, Ann. Sci. École Norm. Sup. (4), No 34, 817-870, 2001. | Zbl | MR | mathdoc-id

[10] H. Donnelly. Quantum unique ergodicity Proc. Amer. Math. Soc. 131:2945-2951, 2003. | Zbl | MR

[11] P. Gérard and E. Leichtnam, Ergodic Properties of Eigenfunctions for the Dirichlet Problem, Duke Mathematical Journal, No 71, 559–607, 1993 | Zbl | MR

[12] A. Haraux. Séries lacunaires et contrôle semi-interne des vibrations d’une plaque rectangulaire, J. Math. Pures Appl. 68-4:457–465, 1989. | Zbl | MR

[13] S. Jaffard Contrôle interne exact des vibrations d’une plaque rectangulaire. Portugal. Math. 47 (1990), no. 4, 423-429. | Zbl | MR

[14] J.P. Kahane Pseudo-périodicité et séries de Fourier lacunaires Annales Sc. de l’Ecole Normale Supérieure 79, 1962. | Zbl | MR | mathdoc-id

[15] J. Marzuola, Eigenfunctions for partially rectangular billiards, in preparation. | Zbl

[16] R.B. Melrose and J. Sjöstrand, Singularities of Boundary Value Problems I & II, Communications in Pure Applied Mathematics, 31 & 35, 593- 617 & 129-168, 1978 & 1982. | Zbl | MR

[17] S. Zelditch. Quantum unique ergodicity. Proc. Amer. Math. Soc. 132:1869-1872, 2004. | Zbl | MR

[18] S. Zelditch and M. Zworski. Ergodicity of eigenfunctions for ergodic billiards. Comm. Math. Phys., 175:673–682, 1996. | Zbl | MR

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