Manuscript XV-B@2 · XV-B.tex · remark · 4d3f12e8

Remark: No automatic identification of ambiguity classes

Supported extension, ambiguity, and closed-set estimates › Extension of finite normal-jet coefficients · lines 1107–1122

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The space (eq:jetambiguity) is the unrestricted supported ambiguity with the fixed response-normal bound. It is not automatically the partial-diagonal class, a normalized contact class, or a space of admissible maps on presentations.

A finite normal-order bound does not make this ambiguity finite-dimensional. For example, when $d \geq 1$ and $Z = {0}$ , already at $r = 0$ the distributions

E_{0} (\partial_{x}^{ν} δ_{0}), ν \in N^{d},

give an infinite linearly independent family. A further bound on the tangential order is needed for a finite-dimensional space.

Displayed formulas in this passage

unlabeled · line 1116
$E_{0} (\partial_{x}^{ν} δ_{0}), ν \in N^{d},$

Nearby in this section

section: Extension of finite normal-jet coefficients
theorem: Theorem: Supported coefficient-extension equivalence
remark: Remark: The concrete order-three interface