Abstract

Let $A$ be the $L^p$ realization of a differential operator $P$ on $\mathbb{R}^n\times \mathbb{R}^+$ with general boundary conditions $B_ku=0$. Here $P$ is a homogeneous polynomial of order $2m$ in $n+1$ complex variables that satisfies a suitable ellipticity condition, and for $1\le k\le m$ $B_k$ is a homogeneous polynomial of order $m_k<2m$; it is assumed that the usual complementing condition is satisfied. We prove that $A$ is a sectorial operator with a bounded $H^\infty $ functional calculus