Wiener-Hopf kernel
= Wiener-Hopf kernel
{c}
{title2=$K(\alpha)$}
The scalar coefficient multiplying an unknown half-line transform in a <Wiener-Hopf equation> is its kernel. This is a transform-domain <function>, distinct from the <null space> of a <linear map>. Its analytic zeros, <poles> and <winding number> govern <Wiener-Hopf factorization>. For mixed scalar Helmholtz half-plane diffraction a typical kernel is the outgoing vertical <wavenumber> $\sqrt{k^2-\alpha^2}$.