= Pole subtraction in a Wiener-Hopf equation
A forcing pole can be split between analytic half-planes by subtracting a factor's value at the pole. For instance,
$$
\frac{L^+(k)}{k+k_0}=\frac{L^+(-k_0)}{k+k_0}
+\frac{L^+(k)-L^+(-k_0)}{k+k_0}.
$$
The second quotient has a removable pole and belongs to the plus expression; the first keeps the prescribed minus-side forcing pole. After <Wiener-Hopf factorization>, analytic continuation identifies an entire remainder, whose value is fixed by growth and edge conditions. The pole prescription must be stated together with the <Fourier transform> convention.
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