Three theorems on third-kind linear integral equations

AbstractConsider a solution space Pτ consisting essentially of linear combinations of continuous functions and poles with integration over the poles defined by Cauchy's principal value. In Pτ the linear integral equation of the third kind is shown to have properties similar to those of the Fredholm equation of the second kind. The space Pτ is a subspace of a solution space Pτ previously studied where no unique solution to the non-homogeneous third-kind equation exists. Solutions in Pτ may be explicitly constructed via Fredholm theory. For simplicity full details are presented only for the case involving a single pole. Generalization to the case of several poles is, however, briefly discussed