Manuscript IX-Free@1 · IX-Free.tex · section · 33b20e96

The individual outputs

F3: construction of the three two-edge distributions › The individual outputs · lines 920–932

IX-Free@1#eq:E1223, IX-Free@1#eq:E1213, IX-Free@1#eq:E1323

Let $V = f \otimes g \otimes f^{'}$ . Define compact distributions on $X$ :

E_{12, 23} [V] E_{12, 13; ν} [V] E_{13, 23; μ} [V] = 2 V K (x, y) K (x^{'}, y), = 2 V K (x, y) S_{0 ν} (x, x^{'}), = 2 V S_{μ 0} (x, x^{'}) K (x^{'}, y) .

Displayed formulas in this passage

IX-Free@1#eq:E1223 · line 924
$E_{12, 23} [V] E_{12, 13; ν} [V] E_{13, 23; μ} [V] = 2 V K (x, y) K (x^{'}, y), = 2 V K (x, y) S_{0 ν} (x, x^{'}), = 2 V S_{μ 0} (x, x^{'}) K (x^{'}, y) .$
IX-Free@1#eq:E1213 · line 924
$E_{12, 23} [V] E_{12, 13; ν} [V] E_{13, 23; μ} [V] = 2 V K (x, y) K (x^{'}, y), = 2 V K (x, y) S_{0 ν} (x, x^{'}), = 2 V S_{μ 0} (x, x^{'}) K (x^{'}, y) .$
IX-Free@1#eq:E1323 · line 924
$E_{12, 23} [V] E_{12, 13; ν} [V] E_{13, 23; μ} [V] = 2 V K (x, y) K (x^{'}, y), = 2 V K (x, y) S_{0 ν} (x, x^{'}), = 2 V S_{μ 0} (x, x^{'}) K (x^{'}, y) .$