On strongly elliptic differential operators on L¹(ℝⁿ)

Abstract

Let $A: = {\Sigma _{\left| \alpha \right| = m}}{a_a}{D^a}$ be a homogeneous differential operator with constant coefficients a_a. Then A is called strongly elliptic if

$$ \operatorname{Re} a\left( \xi \right) > 0{\text{ for }}\xi \in {\mathbb{R}^{n}}\backslash \left\{ 0 \right\}. $$