Inequalities are developed for the fraction of a bandlimited function’s Lₚ norm that can be concentrated on any set of small “Nyquist density.” Two applications are mentioned. First, that a bandlimited function corrupted by impulsive noise can be reconstructed perfectly, provided the noise is concentrated on a set of Nyquist density < 1/π; second, that a wideband signal supported on a set of Nyquist density < 1/ π can be reconstructed stably from noisy data, even when the low-frequency information is completely missing.
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Donoho et al. (1992) studied this question.
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