On Increase at Infinity of Almost Hypoelliptic Polynomials - Ghazaryan, Haik; Margaryan, Vachagan (Eurasian Mathematical Journal, 2013)
It is proved that an almost hypoelliptic polynomial \( P(ξ) = P(ξ_1, …, ξ_n) \) is increasing at infinity, i.e., \( |P(ξ)| → ∞ \) as \( |ξ| → ∞ \), if and only if the number \( n \) of variables of \( P \) is invariant with respect to any linear nondegenerate transformation \( T : \mathbb{R}^n \longrightarrow \mathbb{R}^n \).