# Normal solvability

From Encyclopedia of Mathematics

*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.

#### Comments

#### References

[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) |

**How to Cite This Entry:**

Normal solvability.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Normal_solvability&oldid=17680

This article was adapted from an original article by B.V. Khvedelidze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article