= Paired radial jump of a continuous Cauchy transform
{title2=$\Phi(r\omega)-\Phi(r^{-1}\omega)=P\phi(r\omega)$}
For continuous boundary data on the counterclockwise unit circle and its <Cauchy transform> $\Phi$, $\Phi(r\omega)-\Phi(r^{-1}\omega)=P\phi(r\omega)$ for $0<r<1$. This follows by subtracting the two Cauchy kernels and obtaining the <Poisson kernel on the circle>. Consequently the paired interior-minus-exterior difference tends to $\phi(\omega)$ as $r\uparrow1$. For $r\downarrow1$ from above, the same written difference has the opposite sign. This paired limit does not require each individual boundary value of the transform to exist.
// Destination: analysis.bigb
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