Energies, sum rules and partial decay widths of giant resonances are c
alculated solving exactly the continuum RPA equations corresponding to
a central Woods-Saxon potential. An approximated treatment of those q
uantities in terms of pole expansions of the Green function is also pe
rformed. It is found that the approximated results agree well with the
exact ones. The expansions allow one to understand the microscopic st
ructure of the resonances. Comparison with experimental data is made a
nd a search for physically meaningful resonances is carried out.