  We consider non centered vortices and their arrays in a cylindrically trapped
Bose-Einstein condensate at zero temperature. We study the kinetic energy and
the angular momentum per particle in the Thomas Fermi regime and their
dependence on the distance of the vortices from the center of the trap. Using a
perturbative approach with respect to the velocity-field of the vortices, we
calculate to first order the frequency shift of the collective low-lying
excitations due to the presence of an off-center vortex or a vortex array, and
compare these results with predictions which would be obtained by the
application of a simple sum-rule approach, previously found to be very
successful for centered vortices. It turns out that the simple sum-rule
approach fails for off-centered vortices.
