Let (u(x)=mathbb{1}_{[0,1)}(x)). Show that the Haar-Fourier series for (u) converges for all (1 leqslant p

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Let \(u(x)=\mathbb{1}_{[0,1)}(x)\). Show that the Haar-Fourier series for \(u\) converges for all \(1 \leqslant p<\infty\) in \(L^{p}\)-sense to \(u\). Is this true also for the Haar wavelet expansion?

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