Manuscript IX-C-ST@1 · IX-C-ST.tex · definition · 892f50c4

Definition: One truncated partial product

Whole-domain decomposition and the truncated product › Coefficient definition · lines 2305–2321

IX-C-ST@1#def:product

Let $R_{3} = C [ℏ] / (ℏ^{4})$ . Define

⋆_{c} : D_{decl} ⟶ P_{Σ} \otimes R_{3}, ⋆_{c} (d) = j = 0 \sum^{3} ℏ^{j} C_{j} (d),

and extend $R_{3}$ -linearly to

D_{decl} = D_{decl} \otimes_{C} R_{3} .

A pair of formal functionals is admissible precisely when its tensor over $R_{3}$ lies in this declared formal tensor domain. Its partial product is the value of this linear map.

Displayed formulas in this passage

unlabeled · line 2309
$⋆_{c} : D_{decl} ⟶ P_{Σ} \otimes R_{3}, ⋆_{c} (d) = j = 0 \sum^{3} ℏ^{j} C_{j} (d),$
unlabeled · line 2315
$D_{decl} = D_{decl} \otimes_{C} R_{3} .$

Nearby in this section

section: Coefficient definition
section: Coefficient definition