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Zeitschrift für Analysis und ihre Anwendungen


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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