An introduction to non-harmonic Fourier series

By R. M. Young. 2001

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Shannon sampling and function reconstruction from point values (2004, background): “See [30], and [24] for the multivariate version: Let L < 1/4.”
Meromorphic Inner Functions, Toeplitz Kernels and the Uncertainty Principle (2005, background): “Some other sufficient conditions for completeness are known, as well as some necessary conditions, see [38], [41].”
Some remarks on non-linear approximation with Schauder bases (2001, unknown): “Since the basis is quasi-normed, it is known (see [12]) that there exist constants 0 < A ≤ B < ∞ such that for every f = ∑ k ck(f)gk ∈ X we have A∥{ck(f)}∥l∞ ≤ ∥f∥X ≤ B∥{ck(f)}∥l1 .”
G-frames and G-Riesz Bases (2005, methodology): “, see [20]) that a frame either remains a frame or is incomplete whenever any one of its elements is removed.”
Shannon sampling II: Connections to learning theory (2005, background): “For these basic facts about frames, see [17].”