Manuscript XX-F@1 · XX-F.tex · section · de0bd24f

The displayed finite contact module

Contact normal forms before Newton composition › The displayed finite contact module · lines 1076–1104

XX-F@1#eq:contact, XX-F@1#eq:j

For finite $m$ , consider

b^{ia} (t, y; t^{'}, z) = δ (t - t^{'}) ∣ α ∣ \leq m \sum c_{α}^{ia} (t, y, z) \partial_{y}^{α} δ^{3} (y - z),

with smooth coefficients and compact tangential support. Let the source reconstruction map be $c \mapsto b$ . It is not assumed injective.

Define

j_{γ}^{ia} (t, z) = α \geq γ ∣ α ∣ \leq m \sum (- 1)^{∣ α - γ ∣} (γ α) (\partial_{y}^{α - γ} c_{α}^{ia}) (t, z, z) .

Displayed formulas in this passage

XX-F@1#eq:contact · line 1079
$b^{ia} (t, y; t^{'}, z) = δ (t - t^{'}) ∣ α ∣ \leq m \sum c_{α}^{ia} (t, y, z) \partial_{y}^{α} δ^{3} (y - z),$
XX-F@1#eq:j · line 1094
$j_{γ}^{ia} (t, z) = α \geq γ ∣ α ∣ \leq m \sum (- 1)^{∣ α - γ ∣} (γ α) (\partial_{y}^{α - γ} c_{α}^{ia}) (t, z, z) .$