# Normal solvability

From Encyclopedia of Mathematics

The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

*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.

#### 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=55736

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