  We consider quasi-polynomial spaces of differential forms defined as weighted
(with a positive weight) spaces of differential forms with polynomial
coefficients. We show that the unisolvent set of functionals for such spaces on
a simplex in any spatial dimension is the same as the set of such functionals
used for the polynomial spaces. The analysis in the quasi-polynomial spaces,
however, is not standard and requires a novel approach. We are able to prove
our results without the use of Stokes' Theorem, which is the standard tool in
showing the unisolvence of functionals in polynomial spaces of differential
forms. These new results provide tools for studying exponentially-fitted
discretizations stable for general convection-diffusion problems in Hilbert
differential complexes.
