Manuscript XIV-H@1 · XIV-H.tex · section · 695c7c3a

A source kernel before testing

H2a: the untested local source incidence › A source kernel before testing · lines 733–759

XIV-H@1#eq:sourcepolynomial, XIV-H@1#eq:Qincidence

The actual source is a finite sum of local quadratic monomials. Its full derivative can therefore be written

(J_{D}^{'} [G] h)^{L} (v) = I, J, α, β ∣ α ∣ + ∣ β ∣ \leq 2 \sum q^{L, I, J}_{α β} (v) \partial^{α} G_{J} (v) \partial^{β} h_{I} (v),

where all symmetrization factors are absorbed in $q$ . The smooth coefficients are the fixed coefficients of (eq:actualsource), including the ramp derivatives.

Define the untested incidence kernel

Q^{L, I, J} (v; a, z) = α, β \sum q^{L, I, J}_{α β} (v) \partial_{v}^{α} δ^{(4)} (v - z) \partial_{v}^{β} δ^{(4)} (v - a) .

Displayed formulas in this passage

XIV-H@1#eq:sourcepolynomial · line 737
$(J_{D}^{'} [G] h)^{L} (v) = I, J, α, β ∣ α ∣ + ∣ β ∣ \leq 2 \sum q^{L, I, J}_{α β} (v) \partial^{α} G_{J} (v) \partial^{β} h_{I} (v),$
XIV-H@1#eq:Qincidence · line 750
$Q^{L, I, J} (v; a, z) = α, β \sum q^{L, I, J}_{α β} (v) \partial_{v}^{α} δ^{(4)} (v - z) \partial_{v}^{β} δ^{(4)} (v - a) .$

A source kernel before testing

Displayed formulas in this passage

Nearby in this section