Modified dispersion relations and sum rules

A systematic treatment of modifications to the usual form of dispersion relations and sum rules is given. The treatment is based on the fact that if a function g(z) has analyticity properties analogous to those of a scattering amplitudef (z), the usual dispersion relation for the productf (z)g(z) holds. After having described the general form of the weight function g(z) we concentrate on cases wheng(z) is large in a pre-chosen region and small elsewhere. Weight functions of this type are useful in practical applications where a weight functiong(z) may enhance a contribution of regions where accurate data are available and suppress those of regions with inaccurate or lacking data.Dedicated to Professor V. Votruba on his sixtieth birthday.