✦ LIBER ✦
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
No coin nor oath required. For personal study only.
✦ 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.