On the compactness of certain integral operators

This paper develops practical methods for deciding whether a given kernel function induces a compact integral operator from certain spaces of functions, defined on a compact subset Ω of Rⁿ, into the space of continuous functions over Ω. Necessary and sufficient conditions for compactness are introduced, and several tests for deciding if these conditions are satisfied are developed. The paper concludes with an illustration of the practical use of the theory.