= Signed Cauchy boundary operators
{title2=$P^\pm=\pm I/2+iH/2$}
With $Hv(\rho)=\pi^{-1}\operatorname{PV}\int v(s)/(\rho-s)ds$, the upper and lower limiting <Cauchy integrals> are $P^\pm v=\pm v/2+iHv/2$. They obey $P^+-P^-=I$. The actual complementary idempotent <projections> are $P^+$ and $-P^-$; confusing this signed convention with two positive projectors changes reconstruction signs. These boundary operators naturally enter the <spectral reconstruction of an attenuated Radon transform>.
Back to article page
