Manuscript Em03-D@1 · Em03-D-v1.tex · theorem · 450d878a

Theorem: Quantitative compact-observable transfer

A quantitative transfer estimate from advanced evolution › Conversion to the Unruh moment topology · lines 1320–1346 · proof included or linked

Em03-D@1#thm:transfer, Em03-D@1#eq:transfererror

The exact induced system test satisfies

∥ k (f_{ϵ}) - k_{R} ∥_{U} \leq d_{trf} (R, ϵ) := L_{R} \frac{ϵ ^{2} Λ ^{2}}{1 - z _{ϵ}} ∥ v_{A} ∥_{X} .

The residual probe correction satisfies

∥ k (j_{ϵ}) ∥_{U} \leq L_{R} \frac{Λ}{1 - z _{ϵ}} ∥ v_{A} ∥_{X} .

Proof. Apply Lemma lem:productbound to the two functions in Proposition prop:Neumann, and use $∥ A ∥ \leq Λ$ .

Displayed formulas in this passage

Em03-D@1#eq:transfererror · line 1323
$∥ k (f_{ϵ}) - k_{R} ∥_{U} \leq d_{trf} (R, ϵ) := L_{R} \frac{ϵ ^{2} Λ ^{2}}{1 - z _{ϵ}} ∥ v_{A} ∥_{X} .$
unlabeled · line 1334
$∥ k (j_{ϵ}) ∥_{U} \leq L_{R} \frac{Λ}{1 - z _{ϵ}} ∥ v_{A} ∥_{X} .$