Manuscript I-B-VP@3 · I-B-VP-v3.tex · section · 93c04eb4

Scale-dependent diagonal nonnegative extensions

Scale-dependent diagonal nonnegative extensions · lines 2164–2176

For $0 < ν < 1$ , $λ > 0$ , define $M = M_{λ}$ by

(M /2)^{2 ν} = λ \frac{Γ ( 1 + ν )}{Γ ( 1 - ν )} .

Then

c_{λ} (p) = c_{0} (ν) \frac{p ^{2 ν}}{p ^{2 ν} + M ^{2 ν}} .

Displayed formulas in this passage

unlabeled · line 2168
$(M /2)^{2 ν} = λ \frac{Γ ( 1 + ν )}{Γ ( 1 - ν )} .$
unlabeled · line 2173
$c_{λ} (p) = c_{0} (ν) \frac{p ^{2 ν}}{p ^{2 ν} + M ^{2 ν}} .$