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Finitely-generated solutions of certain integral equations. (English) Zbl 0908.45001

Summary: Recent work has shown that the solutions of the second-kind integral equation arising from a difference kernel can be expressed in terms of two particular solutions of the equation. This paper establishes analogous results for a wider class of integral operators, which includes the special case of those arising from difference kernels, where the solution of the general case is generated by a finite number of particular cases. The generalisation is achieved by reducing the problem to one of finite rank. Certain non-compact operators, including those arising from Cauchy singular kernels, are amenable to this approach.

MSC:

45B05 Fredholm integral equations
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References:

[1] Porter, Integral Equations (1990)
[2] DOI: 10.1216/jiea/1181075634 · Zbl 0747.45001
[3] DOI: 10.1070/RM1980v035n04ABEH001862 · Zbl 0462.45008
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[5] Gohberg, Transl. Math. Monographs 41 (1974)
[6] DOI: 10.1002/cpa.3160210105 · Zbl 0177.39001
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