Manuscript XI-C@1 · XI-C.tex · section · acec1422

Why this is not admission into XI-B's algebra

The joint kernel at fixed regulator width › Why this is not admission into XI-B's algebra · lines 565–580

XI-C@1#eq:finite

Let $P_{fin}$ denote the off-shell polynomial algebra generated by compact smooth linear smearings. Every degree- $n$ kernel in that algebra is a finite sum of smooth tensor products:

u_{n} (x_{1}, \dots, x_{n}) = j = 1 \sum^{N} u_{j 1} (x_{1}) \dots u_{j n} (x_{n}), u_{j i} \in C_{c}^{\infty} (M_{T}^{\circ}) .

The classical limit of XI-B's construction uses precisely this finite-generator presentation before its equation quotient.

Displayed formulas in this passage

XI-C@1#eq:finite · line 570
$u_{n} (x_{1}, \dots, x_{n}) = j = 1 \sum^{N} u_{j 1} (x_{1}) \dots u_{j n} (x_{n}), u_{j i} \in C_{c}^{\infty} (M_{T}^{\circ}) .$

Nearby in this section

proposition: Proposition: The admission distinction is substantive
section: Why this is not admission into XI-B's algebra