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The key step in many Wiener–Hopf problems is to decompose an arbitrary function <math>\Phi</math> into two functions <math>\Phi_{\pm}</math> with the desired properties outlined above. In general, this can be done by writing
: <math>\Phi_+(\alpha) = \frac{1}{2\pi i} \int_{C_1} \Phi(z) \frac{dz}{z-\alpha}</math>
and
<math>\Phi_-(\alpha) = - \frac{1}{2\pi i} \int_{C_2} \Phi(z) \frac{dz}{z-\alpha}</math>,▼
where the contours <math>C_1</math> and <math>C_2</math> are parallel to the real line, but pass above and below the point <math>z=\alpha</math>, respectively.
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