Manuscript Em01-E@2 · Em01-E-v2.tex · definition · 54f8f8c2

Definition: Logarithmically homogeneous chain

Three sufficient verification routes › Route C: an exact translation-origin certificate · lines 1065–1079

For a distribution $H$ on $R^{8}$ , set

H (s \cdot) (ψ) = s^{- 8} H (ψ (\cdot / s)) .

A chain $H_{0}, \dots, H_{J}$ of real degree $λ$ satisfies

H_{j} (s \cdot) = s^{λ} k = 0 \sum^{j} \frac{( lo g s ) ^{k}}{k !} H_{j - k} .

The chain consists of distributions defined at the origin as well as away from it.

Displayed formulas in this passage

unlabeled · line 1067
$H (s \cdot) (ψ) = s^{- 8} H (ψ (\cdot / s)) .$
unlabeled · line 1071
$H_{j} (s \cdot) = s^{λ} k = 0 \sum^{j} \frac{( lo g s ) ^{k}}{k !} H_{j - k} .$