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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