Transfer matrix

The transfer matrix appears in the treatment of refinable functions.

For the mask $h$, which is vector with component indexes from $a$ to $b$, the transfer matrix of $h$, we call it $T_{h}$ here, is defined as

$(T_{h})_{j,k}=h_{2\cdot j-k}$.

More verbosely

$T_{h}={\begin{pmatrix}h_{a}&&&&&\\h_{a+2}&h_{a+1}&h_{a}&&&\\h_{a+4}&h_{a+3}&h_{a+2}&h_{a+1}&h_{a}&\\\ddots &\ddots &\ddots &\ddots &\ddots &\ddots \\&h_{b}&h_{b-1}&h_{b-2}&h_{b-3}&h_{b-4}\\&&&h_{b}&h_{b-1}&h_{b-2}\\&&&&&h_{b}\end{pmatrix}}$