Null-controllability of the Kolmogorov equation in the whole phase space

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Spectral estimates for finite combinations of Hermite functions and null-controllability of hypoelliptic quadratic equations (2018, methodology): “The above geometric condition was introduced by Le Rousseau and Moyano [33] and was shown to be sufficient for the null-controllability of the Kolmogorov equation in any positive time.”
Sharp geometric condition for null-controllability of the heat equation on $$\mathbb {R}^d$$Rd and consistent estimates on the control cost (2017, background): “view the requirements on the control set in the bounded and unbounded case are quite diﬀerent. A suﬃcient condition on control sets for the heat equation on the whole of Rd has been recently given in [LRM16]. In the present paper, we identify a less stringent geometric property on ω which ensures nu”
Observable set, observability, interpolation inequality and spectral inequality for the heat equation in Rn (2017, methodology): “10) was first named as the spectral inequality in [30] (to our best knowledge), it has been studied for long time.”