Difference between revisions of "Normal solvability"
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| − | The property that a [[ | + | 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|integral equation of convolution type]] are normally solvable. |
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====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> S. Goldberg, "Unbounded linear operators" , McGraw-Hill (1966)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> T. Kato, "Perturbation theory for linear operators" , Springer (1980)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> 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)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> S. Goldberg, "Unbounded linear operators" , McGraw-Hill (1966)</TD></TR> | ||
| + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> T. Kato, "Perturbation theory for linear operators" , Springer (1980)</TD></TR> | ||
| + | <TR><TD valign="top">[a3]</TD> <TD valign="top"> 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)</TD></TR> | ||
| + | </table> | ||
Latest revision as of 16:16, 21 April 2024
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
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