by Gorenflo, N., Kunik, M..
Series: 2009-04, Preprints
We present a new and self-contained theory for mapping properties of
the boundary operators for slit diffraction occurring in Sommerfeld’s
diffraction theory, covering two different cases of the polarisation of the
light. This theory is entirely developed in the context of the boundary
operators with a Hankel kernel and not based on the corresponding
mixed boundary value problem for the Helmholtz equation. For a
logarithmic approximation of the Hankel kernel we also study the corresponding
mapping properties and derive explicit solutions together
with certain regularity results.
Sommerfeld diffraction theory, Fourier analysis, Sobolev spaces, mapping properties, boundary integral equations, Hankel functions