Control theory and high energy eigenfunctions
Journées équations aux dérivées partielles (2004), article no. 13, 10 p.
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
@article{JEDP_2004____A13_0,
     author = {Burq, Nicolas and Zworski, Maciej},
     title = {Control theory and high energy eigenfunctions},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {13},
     pages = {1--10},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2004},
     doi = {10.5802/jedp.13},
     mrnumber = {2135608},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jedp.13/}
}
TY  - JOUR
AU  - Burq, Nicolas
AU  - Zworski, Maciej
TI  - Control theory and high energy eigenfunctions
JO  - Journées équations aux dérivées partielles
PY  - 2004
SP  - 1
EP  - 10
PB  - Groupement de recherche 2434 du CNRS
UR  - http://www.numdam.org/articles/10.5802/jedp.13/
DO  - 10.5802/jedp.13
LA  - en
ID  - JEDP_2004____A13_0
ER  - 
%0 Journal Article
%A Burq, Nicolas
%A Zworski, Maciej
%T Control theory and high energy eigenfunctions
%J Journées équations aux dérivées partielles
%D 2004
%P 1-10
%I Groupement de recherche 2434 du CNRS
%U http://www.numdam.org/articles/10.5802/jedp.13/
%R 10.5802/jedp.13
%G en
%F JEDP_2004____A13_0
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://www.numdam.org/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. | MR | Zbl

[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. | MR | Zbl

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[4] N. Burq Control for Schrodinger equations on product manifolds Unpublished, 1992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

[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 | MR | Zbl

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

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

[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. | Numdam | MR | Zbl

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

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

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

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

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

[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. | MR | Zbl

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

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

Cité par Sources :