Manuscript X-C-ST@1 · X-C-ST.tex · definition · b679954e

Definition: Test-level retarded M ller map

Direct construction of the two new maps › Formal inverse on actual tests · lines 652–685

X-C-ST@1#def:moller, X-C-ST@1#eq:moller, X-C-ST@1#eq:second-map, X-C-ST@1#eq:iteration

On actual formal compact tests define

R_{q} = (1 + L [q] E_{A})^{- 1} = 1 - κ L_{1, g} [h] E_{A} + κ^{2} (L_{1, g} [h] E_{A} L_{1, g} [h] E_{A} - L_{2, g} [h, k] E_{A}) .

The inverse is purely formal over $D_{2}$ .

The second-vertex map is

R_{1} (V_{2, g} [h, k]; F_{c}) = ϕ (s_{c} [h, k]), s_{c} [h, k] = - L_{2, g} [h, k] E_{A} c .

The iterated first-vertex coefficient is

\frac{1}{2} R_{2} (V_{1, g} [h], V_{1, g} [h]; F_{c}) = ϕ (i_{c} [h]), i_{c} [h] = L_{1, g} [h] E_{A} L_{1, g} [h] E_{A} c .

The symbol $\frac{1}{2} R_{2}$ denotes this second Taylor coefficient on the diagonal first-vertex family. It does not name a general retarded product.

Displayed formulas in this passage

X-C-ST@1#eq:moller · line 655
$R_{q} = (1 + L [q] E_{A})^{- 1} = 1 - κ L_{1, g} [h] E_{A} + κ^{2} (L_{1, g} [h] E_{A} L_{1, g} [h] E_{A} - L_{2, g} [h, k] E_{A}) .$
X-C-ST@1#eq:second-map · line 667
$R_{1} (V_{2, g} [h, k]; F_{c}) = ϕ (s_{c} [h, k]), s_{c} [h, k] = - L_{2, g} [h, k] E_{A} c .$
X-C-ST@1#eq:iteration · line 675
$\frac{1}{2} R_{2} (V_{1, g} [h], V_{1, g} [h]; F_{c}) = ϕ (i_{c} [h]), i_{c} [h] = L_{1, g} [h] E_{A} L_{1, g} [h] E_{A} c .$

Definition: Test-level retarded M ller map

Displayed formulas in this passage

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