Generalized Vandermonde determinants for reversing Taylor's formula and application to hypoellipticity
Keyword(s):
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.
1983 ◽
Vol 8
(2)
◽
pp. 89-198
◽
1985 ◽
Vol 65
(3)
◽
pp. 150-150
2019 ◽
Vol 31
(3)
◽
pp. 166-191
2007 ◽
Vol 14
(3)
◽
pp. 577-586
◽
1994 ◽
Vol 168
(1)
◽
pp. 19-54
◽