Free Access
Volume 26, 2020
Article Number 9
Number of page(s) 22
Published online 14 February 2020
  1. V. Barbu, A. Răşcanu and G. Tessitore, Carleman estimates and controllability of linear stochastic heat equations. Appl. Math. Optim. 47 (2003) 97–120. [Google Scholar]
  2. J.A. Barcelo, L. Fanelli, S. Gutierrez, A. Ruiz and M.C. Vilela, Hardy uncertainty principle and unique continuation properties of covariant Schrödinger flows. J. Funct. Anal. 264 (2013) 2386–2415. [Google Scholar]
  3. A.F. Bertolin and L. Vega, Uniqueness properties for discrete equations and Carleman estimates. J. Funct. Anal. 264 (2017) 4853–4869. [Google Scholar]
  4. B. Cassano and L. Fanelli, Sharp hardy uncertainty principle and gaussian profiles of covariant Schrödinger evolutions. Trans. Am. Math. Soc. 367 (2015) 2213–2233. [Google Scholar]
  5. M. Cowling, L. Escauriaza, C.E. Kenig, G. Ponce and L. Vega, The hardy uncertainty principle revisited. Indiana Univ. Math. J. 59 (2010) 2007–2025. [CrossRef] [Google Scholar]
  6. M. De Guzman Differentiation of Integrals in ℝn. Measure Theory. Springer, Berlin (1976) 181–185. [CrossRef] [Google Scholar]
  7. L. Escauriaza, C.E. Kenig, G. Ponce and L. Vega, On uniqueness properties of solutions of Schrödinger equations. Commun. Part. Differ. Equ. 264 (2006) 1811–1823. [CrossRef] [Google Scholar]
  8. L. Escauriaza, C.E. Kenig, G. Ponce and L. Vega, Hardy’s uncertainty principle, convexity and Schrödinger evolutions. J. Eur. Math. Soc. 264 (2008) 883–907. [CrossRef] [Google Scholar]
  9. L. Escauriaza, C.E. Kenig, G. Ponce and L. Vega, Uncertainty principle of morgan type and Schrödinger evolutions. J. Lond. Math. Soc. 264 (2010) 187–207. [Google Scholar]
  10. L. Escauriaza, C. Kenig, G. Ponce and L. Vega, Uniqueness properties of solutions to Schrödinger equations. Bull. Am. Math. Soc. 264 (2012) 415–442. [CrossRef] [Google Scholar]
  11. L. Escauriaza, C.E. Kenig, G. Ponce and L. Vega, Hardy uncertainty principle, convexity and parabolic evolutions. Commun. Math. Phys. 346 (2016) 667–678. [CrossRef] [Google Scholar]
  12. L. Escauriaza, C.E. Kenig, G. Ponce, L. Vega et al., The sharp hardy uncertainty principle for Schrödinger evolutions. Duke Math. J. 155 (2010) 163–187. [CrossRef] [Google Scholar]
  13. A. Fernández-Bertolin, Convexity properties of discrete Schrödinger evolutions and hardy’s uncertaintyprinciple (2015). arXiv:1506.03717. [Google Scholar]
  14. F. Flandoli, Regularity Theory and Stochastic Flows for Parabolic SPDES, Vol. 9. CRC Press, Boca Raton (1995). [Google Scholar]
  15. P. Gao, M. Chen and Y. Li, Observability estimates and null controllability for forward and backward linear stochastic Kuramoto–Sivashinsky equations. SIAM J. Control Optim. 53 (2015) 475–500. [Google Scholar]
  16. G.H. Hardy, A theorem concerning Fourier transforms. J. Lond. Math. Soc. 264 (1933) 227–231. [CrossRef] [Google Scholar]
  17. P. Jaming, Y. Lyubarskii, E. Malinnikova and K.-M. Perfekt, Uniqueness for discrete Schrödingerevolutions (2015). arXiv:1505.05398. [Google Scholar]
  18. Q. Lü, Carleman estimate for stochastic parabolic equations and inverse stochastic parabolic problems. Inverse Probl. 264 (2012) 045008. [Google Scholar]
  19. Q. Lu, Observability estimate for stochastic schrödinger equations and its applications. SIAM J. Control Optim. 51 (2013) 121–144. [Google Scholar]
  20. Q. Lü and Z. Yin, Unique continuation for stochastic heat equations. ESAIM: COCV 21 (2015) 378–398. [CrossRef] [EDP Sciences] [Google Scholar]
  21. Q. Lü and X. Zhang, Global uniqueness for an inverse stochastic hyperbolic problem with three unknowns. Commun. Pure Appl. Math. 264 (2015) 948–963. [Google Scholar]
  22. T.A. Nguyen, On a question of Landis and Oleinik. Trans. Am. Math. Soc. 362 (2010) 2875–2899. [Google Scholar]
  23. D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, Vol. 293. Springer Science & Business Media, Berlin (2013). [Google Scholar]
  24. A. Sitaram, M. Sundari and S. Thangavelu, Uncertainty principles on certain lie groups. Proc. Indian Acad. Sci. (Math. Sci.) 105 (1995) 135–151. [CrossRef] [Google Scholar]
  25. E.M. Stein and R. Shakarchi, Complex Analysis. Vol. II of Princeton Lectures in Analysis. Princeton University Press, NJ (2003). [Google Scholar]
  26. G. Wang, M. Wang and Y. Zhang, Observability and unique continuation inequalities for the Schrödingerequation (2016). arXiv:1606.05861. [Google Scholar]
  27. D. Yang and J. Zhong, Observability inequality of backward stochastic heat equations for measurable sets and its applications. SIAM J. Control Optim. 264 (2016) 1157–1175. [Google Scholar]
  28. G. Yuan, Conditional stability in determination of initial data for stochastic parabolic equations. Inverse Probl. 264 (2017) 035014. [Google Scholar]
  29. X. Zhang, Carleman and observability estimates for stochastic wave equations. SIAM J. Math. Anal. 40 (2008) 851–868. [CrossRef] [MathSciNet] [Google Scholar]
  30. X. Zhang, Unique continuation for stochastic parabolic equations. Differ. Integral Equ. 21 (2008) 81–93. [Google Scholar]
  31. E. Zuazua, Controllability and observability of partial differential equations: some results and open problems, in Handbook of Differential Equations: Evolutionary Equations, Vol. 3. Elsevier, North Holland (2007) 527–621. [CrossRef] [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.