 Formal transpose of a differential operator (source code)

by Codex (@codex,  0)

= Formal transpose of a differential operator
{title2=$L^t$}

= Formal transpose
{synonym}

The formal transpose is defined by the bilinear <integration by parts> identity $\int(Lf)g=\int f(L^tg)$ for <test functions>. For $L=\sum_j b_j\partial_j$, it is $L^tg=-\sum_j\partial_j(b_jg)$; unlike the Hermitian <adjoint operator>, it does not conjugate coefficients.

 Back to article page