EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 68 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 68
Number of page(s) 21
DOI https://doi.org/10.1051/cocv/2025042
Published online 19 August 2025
  1. N. Burq and M. Zworski, Control for Schrödinger operators on tori. Math. Res. Lett. 19 (2012) 309–324. [Google Scholar]
  2. N. Burq and M. Zworski, Geometric control in the presence of a black box. J. Am. Math. Soc. 17 (2004) 443–471. [Google Scholar]
  3. L. Miller, Resolvent conditions for the control of unitary groups and their approximations. J. Spectral Theory 2 (2012) 1–55. [Google Scholar]
  4. J. Bourgain and Z. Rudnick, Restriction of total eigenfunctions to hypersurfaces and nodal sets. Geom. Fund. Anal. 22 (2012) 878–937. [Google Scholar]
  5. N. Burq, P. Gerard and N. Tzvetkov, Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds. Duke Math. J. 138 (2007) 445–486. [Google Scholar]
  6. Y. Dermenjian, M. Ben-Artzi and A. Benabdallah, Concentration and non-concentration of eigenfunctions of second-order elliptic operators in layered media. arXiv preprint arXiv:2212.05872 (2022). [Google Scholar]
  7. A. Hassell, L. Hillairet and J. Marzuola, Eigenfunction concentration for polygonal billiards. Commun. Part. Differ. Equ. 34 (2009) 475–485. [Google Scholar]
  8. 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 (1992) 1024–1065. [Google Scholar]
  9. N. Burq, Smoothing effect for Schrodinger boundary value problems. Duke Math. J. 123 (2004) 403. [Google Scholar]
  10. G. Lebeau, Contrôle de l'equation de Schrodinger. J. Math. Pures Appl. 71 (1992) 267–291. [MathSciNet] [Google Scholar]
  11. S. Jaffard, Contrôle interne exact des vibrations d'une plaque rectangulaire. Portugal. Math. 47 (1990) 423–429. [MathSciNet] [Google Scholar]
  12. J. Marzuola, Eigenfunctions for partially rectangular billiards. Commun. Part. Differ. Equ. 31 (2006) 775–790. [Google Scholar]
  13. N. Burq and C. Sun, Time optimal observability for Grushin Schrodinger equation. Anal. PDE 15 (2022) 1487–1530. [Google Scholar]
  14. A. Koenig, Non-null-controllability of the Grushin operator in 2D. Comptes Rendus Math. 355 (2017) 1215–1235. [Google Scholar]
  15. K. Beauchard, P. Cannarsa and R. Guglielmi, Null controllability of Grushin-type operators in dimension two. J. Eur. Math. Soc. 16 (2014) 67–101. [CrossRef] [MathSciNet] [Google Scholar]
  16. K. Beauchard, L. Miller and M. Morancey, 2D grushin-type equations: minimal time and null controllable data. J. Differ. Equ. 259 (2015) 5813–5845. [CrossRef] [Google Scholar]
  17. C. Laurent and M. Leautaud, Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations, Vol. 276. American Mathematical Society (2022). [Google Scholar]
  18. C. Letrouit, Equations sous-elliptiques: contrôle, singularités et théorie spectrale. PhD thesis, Sorbonne universite (2021). [Google Scholar]
  19. J.H. Albert, Topology of the nodal and critical point sets for eigenfunctions of elliptic operators. PhD thesis, Massachusetts Institute of Technology (1971). [Google Scholar]
  20. J.H. Albert, Genericity of simple eigenvalues for elliptic PDE's. Proc. Am. Math. Soc. 48 (1975) 413–418. [Google Scholar]
  21. K. Uhlenbeck, Generic properties of eigenfunctions. Am. J. Math. 98 (1976) 1059–1078. [Google Scholar]
  22. M. Dimassi and J. Sjostrand, Spectral Asymptotics in the Semi-classical Limit. Vol. 268 of Lond. Math. Soc. Lect. Note Ser. Cambridge University Press, Cambridge (1999). [Google Scholar]
  23. B. Helffer, Spectral Theory and its Applications. Vol. 139 of Camb. Stud. Adv. Math. Cambridge University Press, Cambridge (2013). [Google Scholar]
  24. A. Pankov, Introduction to spectral theory of Schrödinger operators. Science Direct Working Paper (2001). [Google Scholar]
  25. L.E. Ballentine, Quantum Mechanics: A Modern Development. World Scientific Publishing Company (2014). [Google Scholar]
  26. P. Glorioso, On common eigenbases of commuting operators. [Google Scholar]
  27. V. Komornik and P. Loreti, Fourier series in Control Theory. Springer Monogr. Math. Springer, New York, NY (2005). [Google Scholar]
  28. V. Komornik and P. Loreti, Fourier series in Control Theory. Springer Monogr. Math. Springer, New York, NY (2005). [Google Scholar]
  29. P.D. Hislop and I.M. Sigal, Introduction to Spectral Theory: With Applications to Schrodinger Operators, Vol. 113. Springer Science & Business Media (2012). [Google Scholar]
  30. M. Zworski, Semiclassical Analysis, Vol. 138. American Mathematical Society (2022). [Google Scholar]
  31. T. Kato, Perturbation Theory for Linear Operators, vol. 132. Springer Science & Business Media (2013). [Google Scholar]
  32. M.H. Harakeh, Spectral Methods In SubRiemannian Geometry. PhD thesis, Universite d'Orléans (2023). [Google Scholar]
  33. K. Knopp, Theory of functions, Parts I and II. Courier Corporation (2013). [Google Scholar]
  34. Y. Saad, Numerical Methods for Large Eigenvalue Problems, revised edn. SIAM (2011). [Google Scholar]
  35. J.L. Kelley, General Topology Vol. 27 of Grad. Texts Math., 2nd edn. Springer, Cham (1975). [Google Scholar]

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.