Manuscript XVI-H@1 · XVI-H.tex · section · af895076

Finite-order continuity on smooth configurations

Finite-order continuity on smooth configurations · lines 1093–1104

The real smooth tensor and scalar spaces carry their compact-set derivative Fréchet topologies. For a compact set $K \subset M$ , define componentwise

p_{r, K} (u) = ∣ α ∣ \leq r max K sup ∣ \partial^{α} u ∣.

The test space $C_{c}^{\infty}$ carries its usual LF topology, not the subspace topology inherited from $C^{\infty}$ .

Displayed formulas in this passage

unlabeled · line 1098
$p_{r, K} (u) = ∣ α ∣ \leq r max K sup ∣ \partial^{α} u ∣.$

Nearby in this section

proposition: Proposition: Joint seminorm estimate
section: Finite-order continuity on smooth configurations