Some remarks on non-linear approximation with Schauder bases

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Nonlinear Approximation with Dictionaries I. Direct Estimates (2004, methodology): “Examples in [GN01] show that a Bernstein inequality cannot hold unless the dictionary is very well structured.”
Greedy Approximation with Regard to Bases and General Minimal Systems (2002, background): “Further investigations ([22, 1, 13, 10]) showed that the concept of greedy bases is very useful in”
The Thresholding Greedy Algorithm, Greedy Bases, and Duality (2003, background): “4 with σn(x) replaced by ‖Hn(x)‖ was proved in [4] (it also follows from Lemmas 2.”
On the existence of almost greedy bases in Banach spaces (2003, unknown): “[6]).”
Frame Decomposition of Decomposition Spaces (2007, background): “[ 27 ]. An important special case of (4.4) is for p = 2 and = 0, where S0 2,2(T,w ) = L2(Rd), and we obtain”
Greedy approximation (2008, methodology): “We note that Approximate Weak Greedy Algorithms in Hilbert spaces were studied in Gribonval and Nielsen (2001a) and Galatenko and Livshitz (2003, 2005).”