Manuscript VII-I@1 · VII-I.tex · section · 907e96ab

Route B1a: field-argument convolution

Route B1a: field-argument convolution · lines 643–660

Choose a real nonnegative even Euclidean-radial compact mollifier $ρ$ , with integral one. Let

S_{ϵ} u = ρ_{ϵ} * u, ρ_{ϵ} (x) = ϵ^{- 4} ρ (x / ϵ) .

At the level of the coordinate construction, define

q_{ϵ} = η + κ S_{ϵ} h + κ^{2} S_{ϵ} k, O_{f, ϵ}^{conv} [h, k, ϕ] = O_{f} [q_{ϵ}, S_{ϵ} ϕ] .

This is not graph-only smoothing.

Displayed formulas in this passage

unlabeled · line 648
$S_{ϵ} u = ρ_{ϵ} * u, ρ_{ϵ} (x) = ϵ^{- 4} ρ (x / ϵ) .$
unlabeled · line 653
$q_{ϵ} = η + κ S_{ϵ} h + κ^{2} S_{ϵ} k, O_{f, ϵ}^{conv} [h, k, ϕ] = O_{f} [q_{ϵ}, S_{ϵ} ϕ] .$