A fredholm study for convolution operators with piecewise continuous symbols on a union of a finite and a semi-infinite intervel¹

¹This research was partly supported by Junta Nacional de investigação Científica e Tecnológica (Portugal) and the Bundesminister für Forschung und Technologie (Germany) wihtin the project Singular Operators - new features and applications

Abstract

We study convolution type operators with kernels that have Fourier transforms in the class of piecewise continuous matrix functions. These convolution operators are assumed to act between Sobolev spaces defined on a union of a finite and a semi-infinite intervel. The main result is a criterion for the Fredholm property of these operators. An application to a problem related to diffraction theory is illustrated.

Keywords:

• Fredholm property
• convolution type operator
• Weiner-Hopf operator
• piecewise continuous Fourier symbol

¹This research was partly supported by Junta Nacional de investigação Científica e Tecnológica (Portugal) and the Bundesminister für Forschung und Technologie (Germany) wihtin the project Singular Operators - new features and applications

¹This research was partly supported by Junta Nacional de investigação Científica e Tecnológica (Portugal) and the Bundesminister für Forschung und Technologie (Germany) wihtin the project Singular Operators - new features and applications

Notes

¹This research was partly supported by Junta Nacional de investigação Científica e Tecnológica (Portugal) and the Bundesminister für Forschung und Technologie (Germany) wihtin the project Singular Operators - new features and applications

Additional information

Notes on contributors

L.P. Castro