Manuscript XVI-D@1 · XVI-D.tex · proposition · b73c6f4a

Proposition: Witness response identification

Explicit witness response and traceless channel · lines 853–870 · proof included or linked

XVI-D@1#lem:identify, XVI-D@1#eq:identify

On $M_{T}$ ,

U_{D} [γ_{1}^{λ}, γ_{2}^{λ}] = R_{λ} = - P V_{λ} .

Proof. Lemma lem:BC and the source input (eq:Slambda) show that the left side solves $L U_{D} = S_{λ}$ with zero initial data. Lemma lem:R gives the same equation and data for $R_{λ}$ . Their difference is a smooth complex homogeneous zero-data solution. Lemma lem:uniqueness makes it zero.

Displayed formulas in this passage

XVI-D@1#eq:identify · line 856
$U_{D} [γ_{1}^{λ}, γ_{2}^{λ}] = R_{λ} = - P V_{λ} .$

Nearby in this section

section: Explicit witness response and traceless channel
lemma: Lemma: Explicit zero-data solution
section: Explicit witness response and traceless channel