  The non autonomous Cauchy problem for time dependent 1D point interactions is
considered. The regularity assumptions for the coupling parameter are
accurately analyzed and show that the general results for non autonomous linear
evolution equations in Banach spaces are far from being optimal. In the mean
time, this article shows an unexpected application of paraproduct techniques,
initiated by J.M. Bony for nonlinear partial differential equations, to a
classical linear problem.
