Manuscript IX-E@1 · IX-E.tex · section · 8f8d5e7f

Admission and support

Prerequisites and entering state › Admission and support · lines 388–428

IX-E@1#eq:admission, IX-E@1#eq:sharp, IX-E@1#eq:support-bounds

Admission includes the IX-A requirement

(D_{η} F)_{h}^{'} (ψ) \in S_{1}, S_{1} = M_{1} + Q_{Σ},

at every smooth configuration and for every finite list of required directions. The admitted coefficient space is treated as a complex vector space stable under conjugation. Admission of required descendants is part of the coefficient requirement, not an automatic consequence of a pairing existing.

The sharp adjoint identity is

C^{*} (θ b) = θ C^{*} b + δ (t) B (b ∣_{Σ}) .

Dropping its second term changes the functional; it is not a presentation rewrite.

Functional support is the closed support of configuration dependence. The imported bounds are

supp_{fun} B_{f} supp_{fun} W_{g} \subset P_{F} \cup F, \subset G, P_{F} = J^{-} (F) \cap {t \geq 0}, F G = supp f, = supp g .

These are upper bounds. Their nonempty intersections do not prove nonempty intersections of the actual functional supports.

Displayed formulas in this passage

IX-E@1#eq:admission · line 391
$(D_{η} F)_{h}^{'} (ψ) \in S_{1}, S_{1} = M_{1} + Q_{Σ},$
IX-E@1#eq:sharp · line 405
$C^{*} (θ b) = θ C^{*} b + δ (t) B (b ∣_{Σ}) .$
IX-E@1#eq:support-bounds · line 415
$supp_{fun} B_{f} supp_{fun} W_{g} \subset P_{F} \cup F, \subset G, P_{F} = J^{-} (F) \cap {t \geq 0}, F G = supp f, = supp g .$