Sommerfeld-watson representation for double-spectral functions - I. Potential scattering without regge poles

We demonstrate the existence of elastically unitary scattering amplitudes, corresponding to a given Born term, when the latter satisfies certain conditions of Höldercontinuity. The results are directly applicable to nonrelativistic potential scattering; and they will also be useful later in connection with the construction of relativistic, crossing-symmetric amplitudes. In this preliminary study, no singularities are allowed in the right half of the complex angular-momentum plane; but it is intended eventually to introduce such singularities (Regge poles and branch-points).