Question: Let B be functions defined on C[0, 1] that are in L2[0, 1]. Define X(f) to be the best approximation to f from the

Let B be functions defined on C[0, 1] that are in L2[0, 1]. Define X(f) to be the best approximation to f from the finite dimensional Haar space AC B. Prove (a) X is a linear operator, (b) X is a projection (X() = X(X())), and (c) ||X||2 = 1. (Hint: Use properties of the L2-inner product)

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