Manuscript Em03-A@1 · Em03-A-v1.tex · assumption · 6d54627d

Assumption: Peeling map and regular affine remainder

A separate late-time limit with a proved remainder · lines 1158–1184

Em03-A@1#ass:peeling, Em03-A@1#eq:peeling, Em03-A@1#eq:affineremainder, Em03-A@1#eq:Cp

Let $p$ be a smooth strictly increasing function for $u \geq u_{0}$ . For constants $A, κ, λ > 0$ , suppose

p (u) = U_{H} - A e^{- κ u} + b (u), ∣ b^{(j)} (u) ∣ \leq B_{j} e^{- (κ + λ) u}, j = 0, 1, 2, 3.

Suppose a positive current state has affine-coordinate covariance

C_{aff} (U, U^{'}) = - \frac{1}{4 π ( U - U ^{'} - i 0 ) ^{2}} + R (U, U^{'}),

where $R$ is smooth and bounded in a neighborhood of $(U_{H}, U_{H})$ .

The pulled-back current covariance is

C_{p} (u, u^{'}) = p^{'} (u) p^{'} (u^{'}) C_{aff} (p (u), p (u^{'})) .

Displayed formulas in this passage

Em03-A@1#eq:peeling · line 1162
$p (u) = U_{H} - A e^{- κ u} + b (u), ∣ b^{(j)} (u) ∣ \leq B_{j} e^{- (κ + λ) u}, j = 0, 1, 2, 3.$
Em03-A@1#eq:affineremainder · line 1170
$C_{aff} (U, U^{'}) = - \frac{1}{4 π ( U - U ^{'} - i 0 ) ^{2}} + R (U, U^{'}),$
Em03-A@1#eq:Cp · line 1179
$C_{p} (u, u^{'}) = p^{'} (u) p^{'} (u^{'}) C_{aff} (p (u), p (u^{'})) .$