Generalized Vandermonde Determinants for Reversing Taylor's Formula and Application to Hypoellipticity

Giuseppe De Donno

《Tamkang Journal of Mathematics》 38卷2期 (2007/06) Pp. 183-189

並列摘要

The problem of the hypoellipticity of the linear partial differential operators with constant coefficients was completely solved by Hörmander 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 Hörmander's hypoellipticity conditions.

並列關鍵字

Vandermonde determinants ； hypoellipticity ； linear partial differential operators