We give a new short proof of H. Landau's density result on necessary conditions for the sampling and interpolation of certain entire functions in the case that the boundary of the spectrum has measure 0. For the proof we adapt a method that has been recently developed by J. Ramanathan and T. Steger in the context of time-frequency analysis. As a consequence of a general theorem for the comparison of densities we obtain several new results about the density of irregular sampling of band-limited functions with derivatives and differential operators.
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Gröchenig et al. (1996) studied this question.