  The use of finite harmonic oscillator spaces in many-body calculations
introduces both infrared (IR) and ultraviolet (UV) errors. The IR effects are
well approximated by imposing a hard-wall boundary condition at a properly
identified radius L_eff. We show that duality of the oscillator implies that
the UV effects are equally well described by imposing a sharp momentum cutoff
at a momentum Lambda_eff complementary to L_eff. By considering two-body
systems with separable potentials, we show that the UV energy corrections
depend on details of the potential, in contrast to the IR energy corrections,
which depend only on the S-matrix. An adaptation of the separable treatment to
more general interactions is developed and applied to model potentials as well
as to the deuteron with realistic potentials. The previous success with a
simple phenomenological form for the UV error is also explained. Possibilities
for controlled extrapolations for A > 2 based on scaling arguments are
discussed.
