In some recent works a dispersion relation proposed by Feshbach for the generalized optical potential has been used in order to analyse the energy dependence of the strength of the empirical optical potential. In the first part of this report the mathematical problems arising in the derivation of the dispersion relation and the results obtained in this direction are discussed; in the second part the approximations introduced in the application of the dispersion relation are analysed and the results concerning the non-locality of the generalized optical potential are reviewed.