Control theory and high energy eigenfunctions

Nicolas Burq[1]; Maciej Zworski[2]

  • [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)

  • page 1-10
  • ISSN: 0752-0360

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Burq, Nicolas, and Zworski, Maciej. "Control theory and high energy eigenfunctions." Journées Équations aux dérivées partielles (2004): 1-10. <http://eudml.org/doc/10592>.

@article{Burq2004,
affiliation = {Université Paris Sud, Mathématiques, Bât 425, 91405 Orsay Cedex; Mathematics Department, University of California. Evans Hall, Berkeley, CA 94720, USA},
author = {Burq, Nicolas, Zworski, Maciej},
journal = {Journées Équations aux dérivées partielles},
keywords = {Dirichlet Laplacian; Neumann Laplacian; periodic Laplacian; eigenfunctions; billiards},
language = {eng},
month = {6},
pages = {1-10},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Control theory and high energy eigenfunctions},
url = {http://eudml.org/doc/10592},
year = {2004},
}

TY - JOUR
AU - Burq, Nicolas
AU - Zworski, Maciej
TI - Control theory and high energy eigenfunctions
JO - Journées Équations aux dérivées partielles
DA - 2004/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 10
LA - eng
KW - Dirichlet Laplacian; Neumann Laplacian; periodic Laplacian; eigenfunctions; billiards
UR - http://eudml.org/doc/10592
ER -

References

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  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. Zbl0786.93009MR1178650
  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 N. Burq Control for Schrodinger equations on product manifolds Unpublished, 1992 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. Zbl1161.81368MR1876933
  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 Zbl0906.93008MR1483711
  7. N. Burq and M. Zworski. Geometric control in the presence of a black box. Jour. Amer. Math. Soc. , 17:443-471, 2004. Zbl1050.35058MR2051618
  8. N. Burq and M. Zworski. Bouncing ball modes and quantum chaos, to appear in SIAM Review, 2004. Zbl1072.81022MR2149100
  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. Zbl1043.35009MR1872422
  10. H. Donnelly. Quantum unique ergodicity Proc. Amer. Math. Soc. 131:2945-2951, 2003. Zbl1027.58024MR1974353
  11. P. Gérard and E. Leichtnam, Ergodic Properties of Eigenfunctions for the Dirichlet Problem, Duke Mathematical Journal, No 71, 559–607, 1993 Zbl0788.35103MR1233448
  12. A. Haraux. Séries lacunaires et contrôle semi-interne des vibrations d’une plaque rectangulaire, J. Math. Pures Appl. 68-4:457–465, 1989. Zbl0685.93039MR1046761
  13. S. Jaffard Contrôle interne exact des vibrations d’une plaque rectangulaire. Portugal. Math. 47 (1990), no. 4, 423-429. Zbl0718.49026MR1090480
  14. J.P. Kahane Pseudo-périodicité et séries de Fourier lacunaires Annales Sc. de l’Ecole Normale Supérieure 79, 1962. Zbl0105.28601MR154060
  15. J. Marzuola, Eigenfunctions for partially rectangular billiards, in preparation. Zbl1127.35029
  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. Zbl0368.35020MR492794
  17. S. Zelditch. Quantum unique ergodicity. Proc. Amer. Math. Soc. 132:1869-1872, 2004. Zbl1055.58016MR2051153
  18. S. Zelditch and M. Zworski. Ergodicity of eigenfunctions for ergodic billiards. Comm. Math. Phys., 175:673–682, 1996. Zbl0840.58048MR1372814

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