09-04
A new and self-contained presentation of the theory of boundary operators for slit diffraction and their logarithmic approximations
Preprint series: 09-04, Preprints
- MSC:
- 78A45 Diffraction, scattering, See also {34E20 for WKB methods}
- 42A50 Conjugate functions, conjugate series, singular integrals
- 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), See also {47B35}
- 45H05 Miscellaneous special kernels, See also {44A15}
Abstract: We present a new and self-contained theory for mapping properties of the boundary operators for slit diffraction occurring in Sommerfeld\x92s 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.
Keywords: Sommerfeld diffraction theory, Fourier analysis, Sobolev spaces, mapping properties, boundary integral equations, Hankel functions
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