  We show that sampling or interpolation formulas in reproducing kernel Hilbert
spaces can be obtained by reproducing kernels whose dual systems form
molecules, ensuring that the size profile of a function is fully reflected by
the size profile of its sampled values. The main tool is a local holomorphic
calculus for convolution-dominated operators, valid for groups with possibly
non-polynomial growth. Applied to the matrix coefficients of a group
representation, our methods improve on classical results on atomic
decompositions and bridge a gap between abstract and concrete methods.
