Manuscript XVI-H@1 · XVI-H.tex · definition · af895076

Definition: Real polarized completion

The polarized completion and witness compatibility · lines 699–715

XVI-H@1#def:Opol, XVI-H@1#eq:Opol

For real smooth $a, c, ϕ$ , define

O_{pol} (a, c; ϕ) = \frac{1}{2} (C_{3, D} (f, g) [a + c, ϕ] - C_{3, D} (f, g) [a, ϕ] - C_{3, D} (f, g) [c, ϕ]) .

This is a polarization of three diagonal completion values, not a definition beginning with an arbitrary polarized response slot.

Displayed formulas in this passage

XVI-H@1#eq:Opol · line 702
$O_{pol} (a, c; ϕ) = \frac{1}{2} (C_{3, D} (f, g) [a + c, ϕ] - C_{3, D} (f, g) [a, ϕ] - C_{3, D} (f, g) [c, ϕ]) .$