Greedy wavelet projections are bounded on BV
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Let BV = BV(d) be the space of functions of bounded variation on d with d 2. Let a;, a; , be a wavelet system of compactly supported functions normalized in BV, i.e., a;BV(d) = 1, a; Each f BV has a unique wavelet expansion a; ca;(f)a; with convergence in L1(d). If AN(f) is the set of N indicies a; for which ca;(f)| are largest (with ties handled in an arbitrary way), then GN(f):= a;AN(f) ca;(f)a; is called a greedy approximation to f. It is shown that GN(f)BV(d) CfBV(d) with C a constant independent of f. This answers in the affirmative a conjecture of Meyer (2001). 2006 American Mathematical Society.