On the line following

“From orthonormality we have”, it seems the upper bound of the summation should be n.

after “A standard heuristic wavelet computation”: it seems that naively plugging in $I=J$ in the summation defining $c_{I,J}$ makes the expression $(\psi_I – \psi_J)^2$ equal to $0$ (interpreting squaring as taking the dot product of the vector with itself). It seems I am missing something simple — any help would be appreciated.

*[Corrected, thanks - T.]*

*[Corrected, thanks - T.]*

*[Corrected, thanks -T]*

*[Either notation is appropriate. In the modern abstract algebra, the multiplicative identity of any ring is often denoted 1, for much the same reason that the additive identity is often denoted 0. -T] *