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

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 operator...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische Nachrichten 2012-01, Vol.285 (1), p.74-102
Main Authors: Gorenflo, Norbert, Kunik, Matthias
Format: Article
Language:English
Subjects:
42A50
45E10
45H05
boundary integral equations
Fourier analysis
Hankel functions
mapping properties
MSC 78A45
Sobolev spaces
Sommerfeld diffraction theory
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.200910203