= Singular integral operator
{title2=$Tf(x)=\operatorname{PV}\int K(x,t)f(t)\,dt$}
A singular <integral> operator has a kernel whose ordinary <integral> can fail at points on the integration domain. A specified limiting prescription, such as a <Cauchy principal value>, can still define the operator by cancellation. For the <Hilbert transform> kernel $1/(t-x)$, subtracting $f(x)$ from a locally Hölder-<continuous> density leaves $[f(t)-f(x)]/(t-x)$ locally integrable; the constant part is interpreted by symmetric deletion. The limiting prescription and the class of allowed densities are part of the operator's definition, not optional details.
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