On Increase at Infinity of Almost Hypoelliptic Polynomials

Abstract

It is proved that an almost hypoelliptic polynomial \( P(\xi) = P(\xi_1, \cdots, \xi_n) \) is increasing at infinity, i.e., \( |P(\xi)| \to \infty \) as \( |\xi| \to \infty \), if and only if the number \( n \) of variables of \( P \) is invariant with respect to any linear nondegenerate transformation \( T : \mathbb{R}^n \longrightarrow \mathbb{R}^n \).