The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (365 KB) | Metadata | Table of Contents | ZAA summary
Volume 22, Issue 3, 2003, pp. 647–687
DOI: 10.4171/ZAA/1167

Published online: 2003-09-30

A Class of Linear Integral Equations and Systems with Sum and Difference Kernel

Lothar von Wolfersdorf

By means of Fourier transform and Cauchy integral techniques a complete investigation of a class of linear integral equations and corresponding systems of equations of cross-correlation type in the Lebesgue spaces L^1 and L^2 is performed. Integral equations of first and second kind are reduced to explicitly solvable Riemann-Hilbert problems for a holomorphic function in the upper half-plane and the system of equations to conjugacy problems for a sectionally holomorphic function, where in the case of a finite interval also the analytic continuation of the solutions to the lower half-plane can be carried out in explicit way. Further, a resolvent representation of the solution to the integral equation and its adjoint equation is derived.

Keywords: Integral equations of correlation type, boundary value problems for holomorphic functions, explicit solutions

von Wolfersdorf Lothar: A Class of Linear Integral Equations and Systems with Sum and Difference Kernel. Z. Anal. Anwend. 22 (2003), 647-687. doi: 10.4171/ZAA/1167