Manuscript XX-D@1 · XX-D.tex · section · c83a526d

External one-contraction products

Native infrared conditions and the cutoff-free theorem › External one-contraction products · lines 1387–1397

For $g \in C_{c}^{\infty} (M; V)$ , define

L_{g} [z] = (z, g)_{0}, w_{g} = W (\cdot, g) .

The Hadamard wavefront relation implies that $w_{g}$ is smooth: compact testing eliminates the singular second-slot covector. It does not imply decay.

Displayed formulas in this passage

unlabeled · line 1390
$L_{g} [z] = (z, g)_{0}, w_{g} = W (\cdot, g) .$

Nearby in this section

assumption: Assumption: External one-rod infrared bound
section: External one-contraction products
theorem: Theorem: Conditional native insertion and regular-probe products
remark: Remark: Status of this theorem