@article{Donno_2007, title={Generalized Vandermonde determinants for reversing Taylor’s formula and application to hypoellipticity}, volume={38}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/89}, DOI={10.5556/j.tkjm.38.2007.89}, abstractNote={The problem of the hypoellipticity of the linear partial differential operators with constant coefficients was completely solved by H"{o}r-man-der in [5]. He listed many equivalent algebraic conditions on the polynomial symbol of the operator, each necessary and sufficient for hypoellipticity. In this paper we employ two Mitchell’s Theorems (1881) regarding a type of Generalized Vandermonde Determinants, for inverting Taylor’s formula of polynomials in several variables with complex coefficients. We obtain then a more direct and easy proof of an equivalence for the mentioned H"{o}r-man-der’s hypoellipticity conditions.}, number={2}, journal={Tamkang Journal of Mathematics}, author={Donno, Giuseppe De}, year={2007}, month={Jun.}, pages={183–189} }