High-Energy Consistency Conditions and Superconvergence Sum Rules

High-energy consistency conditions in the form of superconvergence sum rules are presented for three cases: (1) combinations of partial-wave amplitudes in potential scsttering; (2) a fixed-angle dispersion relation in relativistic theory; (3) partial-wave amplitudes in $\pi N$ scattering. Resonance saturation of the last is attempted. In this approximation, one class of sum rules involving combinations of $f_l\mathrm{}\left(w\right)\mathrm{}$ agrees roughly with experiment; two which are more sensitive to approximation disagree.