Generalized Vandermonde determinants for reversing Taylor's formula and application to hypoellipticity

Authors

  • Giuseppe De Donno

DOI:

https://doi.org/10.5556/j.tkjm.38.2007.89

Abstract

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.

Author Biography

Giuseppe De Donno

Dipartimento di Matematica, Universit`a di Torino, Via Carlo Alberto 10, 10123 Torino, Italy.

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Published

2007-06-30

How to Cite

Donno, G. D. (2007). Generalized Vandermonde determinants for reversing Taylor’s formula and application to hypoellipticity. Tamkang Journal of Mathematics, 38(2), 183-189. https://doi.org/10.5556/j.tkjm.38.2007.89

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Section

Papers