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 706–724

XX-D@1#eq:X

Let

X = C^{\infty} (I; S (R^{3}; V))

with seminorms

p_{J, N, m, β} (z) = t \in J, x sup (1 + ∣ x ∣)^{N} ∣ \partial_{t}^{m} \partial_{x}^{β} z ∣, J ⋐ I .

Use the same domain for the prescribed second jet $ζ$ . Spatially compact smooth configurations are included.

Displayed formulas in this passage

XX-D@1#eq:X · line 709
$X = C^{\infty} (I; S (R^{3}; V))$
unlabeled · line 714
$p_{J, N, m, β} (z) = t \in J, x sup (1 + ∣ x ∣)^{N} ∣ \partial_{t}^{m} \partial_{x}^{β} z ∣, J ⋐ I .$