  The one electron spectral functions for the Luttinger model are discussed for
large but finite systems. The methods presented allow a simple interpretation
of the results. For finite range interactions interesting nonunivesal spectral
features emerge for momenta which differ from the Fermi points by the order of
the inverse interaction range or more. For a simplified model with interactions
only within the branches of right and left moving electrons analytical
expressions for the spectral function are presented which allows to perform the
thermodynamic limit. As in the general spinless model and the model including
spin for which we present mainly numerical results the spectral functions do
not approach the noninteracting limit for large momenta. The implication of our
results for recent high resolution photoemission measurements on quasi
one-dimensional conductors are discussed.
