Manuscript XV-A@1 · XV-A.tex · section · f53f3515

A support-explicit normal-jet theorem

The supported-sector reference and its conditional interface › A support-explicit normal-jet theorem · lines 1256–1277

XV-A@1#eq:insert

The following local theorem makes the conditional extension interface precise and supplies the support qualification needed for its coefficient characterization.

Work in a product normal chart

U = S_{0} \times V, S = S_{0} \times {0}, 0 \in V \subset R^{m},

with coordinates $(x, q)$ . Tests and cutoffs are taken within this chart. For a multi-index $γ$ , define

⟨ E_{γ} b, ϕ ⟩ = (- 1)^{∣ γ ∣} ⟨ b, \partial_{q}^{γ} ϕ (x, 0)⟩, b \in D^{'} (S_{0}) .

Displayed formulas in this passage

XV-A@1#eq:insert · line 1270
$⟨ E_{γ} b, ϕ ⟩ = (- 1)^{∣ γ ∣} ⟨ b, \partial_{q}^{γ} ϕ (x, 0)⟩, b \in D^{'} (S_{0}) .$
unlabeled · line 1263
$U = S_{0} \times V, S = S_{0} \times {0}, 0 \in V \subset R^{m},$

Nearby in this section

definition: Definition: Supported normal order
proposition: Proposition: Finite normal-jet characterization
section: A support-explicit normal-jet theorem
theorem: Theorem: Conditional supported extension interface
remark: Remark: Support is essential to this formulation
section: A support-explicit normal-jet theorem