Normal solvability

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of an integral equation

The property that a linear integral equation is solvable if and only if its right-hand side is orthogonal to all solutions of the corresponding homogeneous adjoint equation. Under appropriate conditions a Fredholm equation, a singular integral equation and an integral equation of convolution type are normally solvable.


[a1] S. Goldberg, "Unbounded linear operators" , McGraw-Hill (1966)
[a2] T. Kato, "Perturbation theory for linear operators" , Springer (1980)
[a3] P.P. Zabreiko (ed.) A.I. Koshelev (ed.) M.A. Krasnoselskii (ed.) S.G. Mikhlin (ed.) L.S. Rakovshchik (ed.) V.Ya. Stet'senko (ed.) T.O. Shaposhnikova (ed.) R.S. Anderssen (ed.) , Integral equations - a reference text , Noordhoff (1975) (Translated from Russian)
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Normal solvability. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by B.V. Khvedelidze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article