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

A concrete unsmoothed classical domain

Native classical domain and distributional operation rules › A concrete unsmoothed classical domain · lines 764–784

XX-D@1#eq:Fclass

The products in (eq:gamma2) and (eq:B12) are Schwartz. The product $B_{1} \partial Y_{1}$ is also Schwartz because $B_{1}$ is Schwartz and $Y_{1}$ has bounded derivatives. Thus $Y_{2}$ is defined on this domain as well.

For $f \in C_{c}^{\infty} (M)$ , set

F_{f} [z, ζ; s] = \int f [\frac{t}{A} + s ℓ z + \frac{s ^{2}}{2} (ℓ ζ + q_{loc} (z) - 2 \calRz \cdot \nabla ℓ z)] d V_{g ˉ} .

Displayed formulas in this passage

XX-D@1#eq:Fclass · line 774
$F_{f} [z, ζ; s] = \int f [\frac{t}{A} + s ℓ z + \frac{s ^{2}}{2} (ℓ ζ + q_{loc} (z) - 2 \calRz \cdot \nabla ℓ z)] d V_{g ˉ} .$

Nearby in this section

section: A concrete unsmoothed classical domain
lemma: Lemma: Native Newton domain and tails
theorem: Theorem: Native classical insertion