ABSTRACT
The following results of the Fredholm theory can be regarded as classical. Let us rewrite Eq. (1.108) as a linear functional equation
(I – µG)u = f , (Gu)(x) = ∫ S
G(x, ξ)u(ξ) ds(ξ). (1.109)
We will consider it in the normal space of continuous functions X = C(S) with the norm ||ϕ||C(S) = maxx∈S |ϕ(x)|. The setU⊂X is called compact if an arbitrary sequence {un}⊂U contains a convergent subsequence.
