Manuscript X-E-ST@1 · X-E-ST.tex · section · 44614221

Topology: smooth tests, distributional kernels, and free classes

Topology: smooth tests, distributional kernels, and free classes · lines 1690–1705

For a compact $A \subset M$ , use

D_{A} = {a \in C_{c}^{\infty} (M; C) : supp a \subset A}, p_{N} (a) = ∣ α ∣ \leq N max sup ∣ \partial^{α} a ∣.

These are ambient smooth fixed-support test spaces, including when $A$ has a nonsmooth boundary. The scalar degree-one quotient is

Q_{m} = D / P_{m} D, D = C_{c}^{\infty} (M; C) .

Displayed formulas in this passage

unlabeled · line 1694
$D_{A} = {a \in C_{c}^{\infty} (M; C) : supp a \subset A}, p_{N} (a) = ∣ α ∣ \leq N max sup ∣ \partial^{α} a ∣.$
unlabeled · line 1702
$Q_{m} = D / P_{m} D, D = C_{c}^{\infty} (M; C) .$