  In a recent article, Schiebinger et al. provided sufficient conditions for
the noiseless recovery of a signal made of M Dirac masses given 2M + 1
observations of, e.g. , its convolution with a Gaussian filter, using the Basis
Pursuit for measures. In the present work, we show that a variant of their
criterion provides a necessary and sufficient condition for the Non-Degenerate
Source Condition (NDSC) which was introduced by Duval and Peyr{\'e} to ensure
support stability in super-resolution. We provide sufficient conditions which,
for instance, hold unconditionally for the Laplace kernel provided one has at
least 2M measurements. For the Gaussian filter, we show that those conditions
are fulfilled in two very different configurations: samples which approximate
the uniform Lebesgue measure or, more surprisingly, samples which are all
confined in a sufficiently small interval.
