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[4] N. Burq Control for Schrodinger equations on product manifolds Unpublished, 1992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