Kernel of an integral operator

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A function in two variables that defines an integral operator by the equality

where ranges over a measure space and belongs to a certain space of functions defined on .



[a1] I.C. Gohberg, S. Goldberg, "Basic operator theory" , Birkhäuser (1981)
[a2] P.R. Halmos, V.S. Sunder, "Bounded integral operators on spaces" , Springer (1978)
[a3] K. Jörgens, "Lineare Integraloperatoren" , Teubner (1970)
[a4] V.I. Smirnov, "A course of higher mathematics" , 4 , Addison-Wesley (1964) (Translated from Russian)
[a5] 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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Kernel of an integral operator. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by G.L. Litvinov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article