Manuscript Em03-F@1 · Em03-F-v1.tex · section · 0d4d148b

A compact-test estimate

Exterior field, scattering coordinates, and infrared control › A compact-test estimate · lines 475–488

Em03-F@1#eq:Bbound

Define

A_{0} = \frac{1}{2} + \frac{2}{β ω _{c}}, A_{1} = \frac{1}{2 ω _{c} ^{2}} + \frac{2}{3 β ω _{c} ^{3}},

B_{X} (f)^{2} = \frac{C _{X} ^{2}}{2 π} (A_{0} ∥ f ∥_{1}^{2} + A_{1} ∥ \partial_{t} f ∥_{1}^{2}) .

Displayed formulas in this passage

Em03-F@1#eq:Bbound · line 482
$B_{X} (f)^{2} = \frac{C _{X} ^{2}}{2 π} (A_{0} ∥ f ∥_{1}^{2} + A_{1} ∥ \partial_{t} f ∥_{1}^{2}) .$
unlabeled · line 478
$A_{0} = \frac{1}{2} + \frac{2}{β ω _{c}}, A_{1} = \frac{1}{2 ω _{c} ^{2}} + \frac{2}{3 β ω _{c} ^{3}},$