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

Diagonal response theorem

The two inherited interfaces and no-decay uniqueness › Diagonal response theorem · lines 516–542

XVI-D@1#eq:response

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The supplied XII-D response statement is:

For every smooth $γ$ , the response formula defines a unique smooth zero-initial-data solution on the slab.

The reported Section D0 also states:

No spatial decay is required.

Its response formula is

u_{D} [γ] = - P E_{0}^{R} (J_{D} [γ]), L u_{D} [γ] = J_{D} [γ] .

The reported construction is local near compact observation sets and independent of its auxiliary spatial cutoff XIID.

We use its existence assertion on real smooth metric perturbations. We do not infer the scope of uniqueness solely from the phrase concerning spatial decay: the needed uniqueness class is established directly next.

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XVI-D@1#eq:response · line 528
$u_{D} [γ] = - P E_{0}^{R} (J_{D} [γ]), L u_{D} [γ] = J_{D} [γ] .$

Diagonal response theorem

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