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

F3: construction of the three two-edge distributions

F3: construction of the three two-edge distributions · lines 819–831

Put

S_{μν} (x, x^{'}) = \partial_{μ}^{x} \partial_{ν}^{x^{'}} Δ_{m}^{+} (x - x^{'}), m \geq 0.

We use the standard product, submersion-pullback, and proper pushforward calculus for distributions Hormander,Demanet. The graph-specific covector checks are proved below.

Displayed formulas in this passage

unlabeled · line 823
$S_{μν} (x, x^{'}) = \partial_{μ}^{x} \partial_{ν}^{x^{'}} Δ_{m}^{+} (x - x^{'}), m \geq 0.$