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.

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关于微分形式的拟多项式空间的不解性

我们考虑定义为具有多项式系数的微分形式的加权（具有正权重）空间的微分形式的拟多项式空间。我们表明，在任何空间维度上的单纯形上的此类空间的单解泛函集与用于多项式空间的此类泛函集相同。然而，准多项式空间中的分析不是标准的，需要一种新颖的方法。我们能够在不使用斯托克斯定理的情况下证明我们的结果，斯托克斯定理是显示微分形式多项式空间中泛函不解的标准工具。这些新结果为研究对 Hilbert 微分复合中的一般对流扩散问题稳定的指数拟合离散化提供了工具。