Manuscript X-A-conv@1 · X-A-conv.tex · section · c76fffa3

First coordinate kernel

Smooth coefficient kernels, support, and continuity › First coordinate kernel · lines 1371–1389

X-A-conv@1#eq:Lambda

For a tensor component label $A = (α β)$ , let $e_{A}$ denote the constant symmetric component basis. Define

H_{A, y} (u) = g (y) ϱ_{ε} (u - y) e_{A} .

Then

Λ_{A}^{μ} (z, y) = [E_{0} C H_{A, y}]^{μ} (z)

is the first coordinate kernel:

w^{μ} [h] (z) = \int Λ_{A}^{μ} (z, y) h_{A} (y) d^{4} y .

Displayed formulas in this passage

X-A-conv@1#eq:Lambda · line 1379
$Λ_{A}^{μ} (z, y) = [E_{0} C H_{A, y}]^{μ} (z)$
unlabeled · line 1375
$H_{A, y} (u) = g (y) ϱ_{ε} (u - y) e_{A} .$
unlabeled · line 1386
$w^{μ} [h] (z) = \int Λ_{A}^{μ} (z, y) h_{A} (y) d^{4} y .$