Manuscript I-B-G@2 · I-B-G-v2.tex · section · 3b4d700f

The geometric arrival window

Supported replacement of flat-completion operators › The geometric arrival window · lines 1648–1665

I-B-G@2#eq:Tarr

For spatial pairs in such a chart, define

T_{arr} (x, x^{'}) = min ({ρ_{0}} \cup {R_{k} : k \neq = 0, ∣ ψ - 2 π α k ∣ \leq π}) .

Including the equality case does not change the threshold: such a term has $R_{k} = ρ_{0}$ . This definition records all possible additional geometric arrivals, whether or not their total coefficient later cancels.

Displayed formulas in this passage

I-B-G@2#eq:Tarr · line 1651
$T_{arr} (x, x^{'}) = min ({ρ_{0}} \cup {R_{k} : k \neq = 0, ∣ ψ - 2 π α k ∣ \leq π}) .$

Nearby in this section

definition: Definition: Angularly small chart
lemma: Lemma: Uniform lower bound
theorem: Theorem: Scalar kernel replacement
remark: Remark: A sufficient window, not a universal converse