On formally almost hypoelliptic polynomials of constant power

摘要

In this paper we study properties of differential operators (polynomials) with variable coefficients of constant power or of constant strength in the sense of L. Hormander. Necessary conditions for constancy of the strength and power of polynomials of many variables are obtained. For polynomials of two variables with real coefficients necessary and sufficient conditions for constancy of the power and for formally almost hypoellipticity, in terms of zeros and their multiplicities of the corresponding generalized-homogeneous subpolynomials of underlying polynomials are also obtained.