  We prove quantitative spectral inequalities for the (anisotropic) Shubin
operators on the whole Euclidean space, thus relating for functions from
spectral subspaces associated to finite energy intervals their $L^2$-norm on
the whole space to the $L^2$-norm on a suitable subset. A particular feature of
our estimates is that the constant relating these $L^2$-norms is very explicit
in geometric parameters of the corresponding subset of the whole space, which
may become sparse at infinity and may even have finite measure. This extends
results obtained recently by J. Martin and, in the particular case of the
harmonic oscillator, by A. Dicke, I. Veseli\'c, and the second author. We apply
our results towards null-controllability of the associated parabolic equations,
as well as to the ones associated to the (degenerate) Baouendi-Grushin
operators acting on $\mathbb R^d \times \mathbb T^d$.
