Manuscript XVI-K@1 · XVI-K.tex · section · aa7553bb

Restoring the smooth coefficients

A coherent extension map on the finite span › Restoring the smooth coefficients · lines 1461–1490

XVI-K@1#eq:QKext

Let

q^{R_{K}} ˉ_{k} = R_{K} (q^{\circ}_{k}), r_{2} (y, w) = y - w .

The extended selected-sector distribution is

Q_{K}^{μν} (y, w; h) = k \in N \sum a^{μν}_{k} (y, w; h) r_{2}^{*} q^{R_{K}} ˉ_{k} .

The operations are, in order:

extend in z ⟶ pull back by z = y - w ⟶ multiply by the smooth coefficient .

Submersion pullback and smooth multiplication define this finite sum. Its restriction to $y \neq = w$ is (eq:QK). No $y$ - or $w$ -dependent coefficient enters $R_{K}$ .

Displayed formulas in this passage

XVI-K@1#eq:QKext · line 1470
$Q_{K}^{μν} (y, w; h) = k \in N \sum a^{μν}_{k} (y, w; h) r_{2}^{*} q^{R_{K}} ˉ_{k} .$
unlabeled · line 1464
$q^{R_{K}} ˉ_{k} = R_{K} (q^{\circ}_{k}), r_{2} (y, w) = y - w .$
unlabeled · line 1479
$extend in z ⟶ pull back by z = y - w ⟶ multiply by the smooth coefficient .$