Continuous frames for unbounded operators

Few years ago Găvruţa gave the notions of K-frame and atomic system for a linear bounded operator K in a Hilbert space H in order to decompose 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 A on a Hilbert space in a continuous setting, thus extending what have been done in a previous paper in a discrete framework