The paper studies bounded or unbounded operators which can act as analysis operators or synthesis operators of various signal processing including generalized frames, semi-frames, discrete frames, Fourier transforms, etc. The paper is concluded by a short discussion of the controllability of the behavior of the processed signals.
"Unbounded analysis operators." Bull. Belg. Math. Soc. Simon Stevin 20 (1) 123 - 132, february 2013. https://doi.org/10.36045/bbms/1366306718