Generalized Fourier frames in terms of balayage

Based on Beurling's theory of balayage, we develop the theory of non-uniform sampling in the context of the theory of frames for the settings of the Short Time Fourier Transform and pseudo-differential operators. There is sufficient complexity to warrant new examples generally, and to resurrect the formulation of balayage in terms of covering criteria with an eye towards an expanded theory as well as computational implementation.