Manuscript XVI-K@1 · XVI-K.tex · section · aa7553bb

Individual bounds and coherent changes

Prescription ambiguity and propagated contact terms › Individual bounds and coherent changes · lines 1762–1782

Independent choices satisfying only (eq:Dq) still define an attached expression for the fixed decomposition (eq:QKext). They need not constitute a coherent alternative extension map. The propagated formula below is valid in either case.

For a coherent change and $u \in H_{k}$ , the coefficients can be recovered from moments:

(R_{K}^{'} - R_{K}) (u) = ∣ γ ∣ \leq k - 4 \sum c_{γ} (u) \partial^{γ} δ, c_{γ} (u) = (- 1)^{∣ γ ∣} ⟨ (R_{K}^{'} - R_{K}) (u), w^{(k - 4)}_{γ} ⟩ .

Thus a change of subtraction function or declared moments is included in this ambiguity description.

Displayed formulas in this passage

unlabeled · line 1772
$(R_{K}^{'} - R_{K}) (u) = ∣ γ ∣ \leq k - 4 \sum c_{γ} (u) \partial^{γ} δ, c_{γ} (u) = (- 1)^{∣ γ ∣} ⟨ (R_{K}^{'} - R_{K}) (u), w^{(k - 4)}_{γ} ⟩ .$

Nearby in this section

proposition: Proposition: Point-supported changes