Manuscript I-B-VP-1@1 · I-B-VP-1-v1.tex · definition · 6d700be9

Definition: Generating finite part

Strong radial finite parts › The scalar generating distribution · lines 490–502

I-B-VP-1@1#def:U, I-B-VP-1@1#eq:Uepsilon

Define

U_{L, ε}^{ρ} = ρ (r / ε) r^{- 2} + σ_{α} (lo g \frac{ε}{L} - c_{ρ}) δ_{W} .

Its limit will be denoted by $U_{L}$ . The first term is interpreted as a locally integrable function with the density $d Ω$ .

Displayed formulas in this passage

I-B-VP-1@1#eq:Uepsilon · line 493
$U_{L, ε}^{ρ} = ρ (r / ε) r^{- 2} + σ_{α} (lo g \frac{ε}{L} - c_{ρ}) δ_{W} .$