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A new and self-contained presentation of the theory of boundary operators for slit diffraction and their logarithmic approximations

✍ Scribed by Norbert Gorenflo; Matthias Kunik


Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
279 KB
Volume
285
Category
Article
ISSN
0025-584X

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✦ Synopsis


Abstract

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.