Generalization of Bochner's theorem for functions of the positive type

We generalize Bochner's theorem for functions of the positive type-theorem 1-to more general integral transforms using the Jost solution of the radial Schroedinger equation. The generalized theorem is theorem 2. We then use Bochner's theorem to obtain an integral representation for the phase shift, shown in theorem 4. In a forthcoming paper, this theorem will be used in inverse scattering theory. The proofs are simple, and make use of well-known theorems of real analysis and Fourier transforms of L1, L1 intersection L2, ... functions