A new and self-contained presentation of the theory of boundary operators for slit diffraction and their logarithmic approximations
Corresponding Author
Norbert Gorenflo
Beuth Hochschule für Technik Berlin, Fachbereich II, Luxemburger Strasse 10, 13353 Berlin, Germany
Norbert Gorenflo, Phone: +49 30 4504 2267, Fax: +49 30 4504 2011
Matthias Kunik, Otto-von-Guericke-Universität, Institut für Analysis und Numerik, Universitätsplatz 2, 39106 Magdeburg, Germany. Phone: +49 391 67 12877, Fax: +49 391 67 18073
Search for more papers by this authorCorresponding Author
Matthias Kunik
Otto-von-Guericke-Universität, Institut für Analysis und Numerik, Universitätsplatz 2, 39106 Magdeburg, Germany
Norbert Gorenflo, Phone: +49 30 4504 2267, Fax: +49 30 4504 2011
Matthias Kunik, Otto-von-Guericke-Universität, Institut für Analysis und Numerik, Universitätsplatz 2, 39106 Magdeburg, Germany. Phone: +49 391 67 12877, Fax: +49 391 67 18073
Search for more papers by this authorCorresponding Author
Norbert Gorenflo
Beuth Hochschule für Technik Berlin, Fachbereich II, Luxemburger Strasse 10, 13353 Berlin, Germany
Norbert Gorenflo, Phone: +49 30 4504 2267, Fax: +49 30 4504 2011
Matthias Kunik, Otto-von-Guericke-Universität, Institut für Analysis und Numerik, Universitätsplatz 2, 39106 Magdeburg, Germany. Phone: +49 391 67 12877, Fax: +49 391 67 18073
Search for more papers by this authorCorresponding Author
Matthias Kunik
Otto-von-Guericke-Universität, Institut für Analysis und Numerik, Universitätsplatz 2, 39106 Magdeburg, Germany
Norbert Gorenflo, Phone: +49 30 4504 2267, Fax: +49 30 4504 2011
Matthias Kunik, Otto-von-Guericke-Universität, Institut für Analysis und Numerik, Universitätsplatz 2, 39106 Magdeburg, Germany. Phone: +49 391 67 12877, Fax: +49 391 67 18073
Search for more papers by this authorAbstract
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.
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