  Using his formulation of the potential theoretic notion of balayage and his
deep results about this idea, Beurling gave sufficient conditions for Fourier
frames in terms of balayage. The analysis makes use of spectral synthesis, due
to Wiener and Beurling, as well as properties of strict multiplicity, whose
origins go back to Riemann. In this setting and with this technology, we
formulate and prove non-uniform sampling formulas in the context of the short
time Fourier transform (STFT).
