In this paper we study some aspects of oblique duality between finite
sequences of vectors \cF and \cG lying in finite dimensional subspaces
\cW and \cV, respectively. We compute the possible eigenvalue lists of the
frame operators of oblique duals to \cF lying in \cV; we then compute the
spectral and geometrical structure of minimizers of convex potentials among
oblique duals for \cF under some restrictions. We obtain a complete
quantitative analysis of the impact that the relative geometry between the
subspaces \cV and \cW has in oblique duality. We apply this analysis to
compute those rigid rotations U for \cW such that the canonical oblique
dual of U\cdot \cF minimize every convex potential; we also introduce a
notion of aliasing for oblique dual pairs and compute those rigid rotations U
for \cW such that the canonical oblique dual pair associated to U\cdot \cF
minimize the aliasing. We point out that these two last problems are intrinsic
to the theory of oblique duality.Comment: 23 page