Addition of lower order terms preserving almost hypoellipticity of polynomials

Abstract

A linear differential operator \(P(D)\) with constant coefficients is called almost hypoelliptic if all derivatives \(P^{(\nu)}(\xi)\) of the characteristic polynomial \(P(\xi)\) can be estimated above via \(P(\xi)\). In this paper we describe the collection of lower order terms addition of which to an almost hypoelliptic operator \(P(D)\) (polynomial \(P(\xi)\)) preserves its almost hypoellipticity and its strength.