  Few years ago G\u{a}vru\c{t}a gave the notions of $K$-frame and atomic system
for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$ in order to
decompose $\mathcal{R}(K)$, the range of $K$, with a frame-like expansion.
These notions are here generalized to the case of a densely defined and
possibly unbounded operator on a Hilbert space $A$ in a continuous setting,
thus extending what have been done in a previous paper in a discrete framework.
