Let $$\psi_{j,k}(t)=\begin{cases} 2^{j/2}, & 2^{-j}k < t < 2^{-j}(k+1/2)\\-2^{j/2} ,& 2^{-j}(k+1/2) < t < 2^{-j}(k+1) \\ 0, & \textrm{otherwise.} \end{cases}$$ How to prove that it is orthogonal? In other words how to prove that $\langle \psi_{j_1,k_1}(t), \psi_{j_2, k_2}(t) \rangle = 0$, $j_1
Let $\{ \psi_{j,k}(t)\}$ haar system. How to prove that it is orthogonal?
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linear-algebra