Manuscript Em02-D@4 · Em02-D-v4.tex · section · fcf2fac7

Boundary/interior decomposition

Exact signed internal convolution for 5z › Boundary/interior decomposition · lines 1562–1581

For $s = (q, q n)$ , let

G_{j}^{r} [v] = (D_{p}^{j} Γ_{int}) (S; v)_{S = s} .

Thus

G_{0}^{r} [v] = \frac{1}{8 π} \int_{0}^{1} v (λ s) d λ, G_{1}^{r} [v] = A^{r} [v],

where $A^{r}$ is (eq:A) with $x$ replaced by $r$ . Write $Γ_{j}^{r} (S; v) = D_{p}^{j} Γ_{int} (S; v)$ .

Displayed formulas in this passage

unlabeled · line 1565
$G_{j}^{r} [v] = (D_{p}^{j} Γ_{int}) (S; v)_{S = s} .$
unlabeled · line 1572
$G_{0}^{r} [v] = \frac{1}{8 π} \int_{0}^{1} v (λ s) d λ, G_{1}^{r} [v] = A^{r} [v],$