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All issues Volume 29 (2023) ESAIM: COCV, 29 (2023) 80 References
Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 80
Number of page(s) 35
DOI https://doi.org/10.1051/cocv/2023063
Published online 08 November 2023
  1. P. Alphonse and J. Bernier, Polar decomposition of semigroups generated by non-selfadjoint quadratic differential operators and regularizing effects. Ann. Sci. Éc. Norm. Supér. 56 (2023) 323–382. [CrossRef] [MathSciNet] [Google Scholar]
  2. P. Alphonse, Null-controllability of evolution equations associated with fractional Shubin operators through quantitative Agmon estimates. Preprint: arXiv:2012.04374. [Google Scholar]
  3. P. Alphonse, Quadratic differential equations: partial Gelfand–Shilov smoothing effect and null-controllability. J. Inst. Math. Jussieu 20 (2021) 1749–1801. [CrossRef] [MathSciNet] [Google Scholar]
  4. K. Beauchard, M. Egidi and K. Pravda-Starov, Geometric conditions for the null-controllability of hypoelliptic quadratic parabolic equations with moving control supports. C. R. Math. Acad. Sci. Paris 358 (2020) 651–700. [MathSciNet] [Google Scholar]
  5. K. Beauchard, P. Jaming and K. Pravda-Starov, Spectral estimates for finite combinations of Hermite functions and null-controllability of hypoelliptic quadratic equations. Studia Math. 260 (2021) 1–43. [CrossRef] [MathSciNet] [Google Scholar]
  6. K. Beauchard and K. Pravda-Starov, Null-controllability of hypoelliptic quadratic differential equations. J. Éc. polytech. Math. 5 (2018) 1–43. [CrossRef] [MathSciNet] [Google Scholar]
  7. R.P. Boas, Entire functions. Academic Press Inc., New York (1954). [Google Scholar]
  8. J.M. Coron, Control and Nonlinearity, Vol. 136 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (2007). [Google Scholar]
  9. A. Dicke, A. Seelmann and I. Veselić, Uncertainty principle for Hermite functions and null-controllability with sensor sets of decaying density. J. Fourier Anal. Appl. 29 (2023) 11. [CrossRef] [Google Scholar]
  10. A. Dicke, A. Seelmann and I. Veselić, Spectral inequality with sensor sets of decaying density for Schrödinger operators with power growth potentials. Preprint: arXiv:2206.08682. [Google Scholar]
  11. M. Egidi, I. Nakić, A. Seelmann, M. Täufer, M. Tautenhahn and I. Veselić, Null-controllability and control cost estimates for the heat equation on unbounded and large bounded domains, in Control Theory of Infinite-Dimensional Systems, edited by J. Kerner, H. Laasri and D. Mugnolo. Springer International Publishing, Cham (2020) 117–157. [CrossRef] [Google Scholar]
  12. M. Egidi and A. Seelmann, An abstract Logvinenko–Sereda type theorem for spectral subspaces. J. Math. Anal. Appl. 500 (2021) 125149. [CrossRef] [Google Scholar]
  13. M. Egidi and I. Veselić, Sharp geometric condition for null-controllability of the heat equation on ℝd and consistent estimates on the control cost. Arch. Math. (Basel) 111 (2018) 85–99. [CrossRef] [MathSciNet] [Google Scholar]
  14. M. Egidi and I. Veselić, Scale-free unique continuation estimates and Logvinenko–Sereda theorems on the torus. Ann. Henri Poincaré 21 (2020) 3757–3790. [CrossRef] [MathSciNet] [Google Scholar]
  15. D. Gallaun, C. Seifert and M. Tautenhahn, Sufficient criteria and sharp geometric conditions for observability in Banach spaces. SIAM J. Control Optim. 58 (2020) 2639–2657. [CrossRef] [MathSciNet] [Google Scholar]
  16. M. Hitrik and K. Pravda-Starov, Spectra and semigroup smoothing for non-elliptic quadratic operators. Math. Ann. 344 (2009) 801–846. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Hitrik, K. Pravda-Starov and J. Viola, From semigroups to subelliptic estimates for quadratic operators. Trans. Am. Math. Soc. 370 (2018) 7391–7415. [CrossRef] [Google Scholar]
  18. L. Hörmander, Symplectic classification of quadratic forms, and general Mehler formulas. Math. Z. 219 (1995) 413–449. [CrossRef] [MathSciNet] [Google Scholar]
  19. F. John, Extremum problems with inequalities as subsidiary conditions, in Studies and Essays Presented to R. Courant on his 60th Birthday, January 8, 1948. Interscience Publishers, Inc., New York, N.Y. (1948) 187–204. [Google Scholar]
  20. H. Jung, Ueber die kleinste Kugel, die eine räumliche Figur einschliesst. J. Reine Angew. Math. 123 (1901) 241–257. [MathSciNet] [Google Scholar]
  21. V.È. Kacnel’son, Equivalent norms in spaces of entire functions, Mat. Sb. (N.S.) 92 (1973) 34–54. [MathSciNet] [Google Scholar]
  22. A. Kolmogoroff, Zufällige Bewegungen. (Zur Theorie der Brownschen Bewegung.). Ann. Math. 35 (1934) 116–117. [CrossRef] [MathSciNet] [Google Scholar]
  23. O. Kovrijkine, Some estimates of Fourier transforms. Ph.D. Thesis, California Institute of Technology, ProQuest LLC, Ann Arbor, MI (2000). [Google Scholar]
  24. O. Kovrijkine, Some results related to the Logvinenko-Sereda theorem. Proc. Am. Math. Soc. 129 (2001) 3037–3047. [CrossRef] [Google Scholar]
  25. J. Le Rousseau and I. Moyano, Null-controllability of the Kolmogorov equation in the whole phase space. J. Differ. Equ. 260 (2016) 3193–3233. [CrossRef] [Google Scholar]
  26. V.N. Logvinenko and J.F. Sereda, Equivalent norms in spaces of entire functions of exponential type. Teor. Funkciĭ Funkcional. Anal. Priložen. 20 (1974) 102–111. [Google Scholar]
  27. J. Martin, Spectral inequalities for anisotropic Shubin operators. Preprint: arXiv:2205.11868. [Google Scholar]
  28. J. Martin and K. Pravda-Starov, Spectral inequalities for combinations of Hermite functions and null-controllability for evolution equations enjoying Gelfand–Shilov smoothing effects. J. Inst. Math. Jusieu (2022) 1–50. [Google Scholar]
  29. L. Miller, Unique continuation estimates for sums of semiclassical eigenfunctions and null-controllability from cones. Preprint: HAL:00411840. [Google Scholar]
  30. I. Nakić, M. Täufer, M. Tautenhahn and I. Veselić, Sharp estimates and homogenization of the control cost of the heat equation on large domains. ESAIM Control Optim. Calc. Var. 26 (2020) 26. [CrossRef] [EDP Sciences] [Google Scholar]
  31. F.L. Nazarov, Local estimates for exponential polynomials and their applications to inequalities of the uncertainty principle type. Algebra Analiz 5 (1993) 3–66. [Google Scholar]
  32. F. Nicola and L. Rodino, Global Pseudo-differential Calculus on Euclidean Spaces, Vol. 4. Birkhäuser, Basel (2010). [CrossRef] [Google Scholar]
  33. K. Schmüdgen, Unbounded Self-adjoint Operators on Hilbert Space, Vol. 265. Springer, Dordrecht (2012). [CrossRef] [Google Scholar]
  34. A. Seelmann, The Laplacian on Cartesian products with mixed boundary conditions. Arch. Math. 117 (2021) 87–94. [CrossRef] [MathSciNet] [Google Scholar]
  35. G. Tenenbaum and M. Tucsnak, On the null-controllability of diffusion equations. ESAIM Control Optim. Calc. Var. 17 (2011) 1088–1100. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  36. M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups. Birkhäuser Advanced Texts: Basler Lehrbücher. Birkhäuser Verlag, Basel (2009). [CrossRef] [Google Scholar]
  37. G. Wang, M. Wang, C. Zhang and Y. Zhang, Observable set, observability, interpolation inequality and spectral inequality for the heat equation in ℝn. J. Math. Pures Appl. 126 (2019) 144–194. [CrossRef] [MathSciNet] [Google Scholar]
  38. J. Weidmann, Linear Operators in Hilbert Spaces. Transl. by Joseph Szücs, Vol. 68. Springer, New York, NY (1980). [CrossRef] [Google Scholar]
  39. E. Zuazua. Controllability of Partial Differential Equations. Lecture, URL: https://cel.archives-ouvertes.fr/cel-00392196, August 2006. [Google Scholar]

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