Hörmander staircase

Let $P({\xi }^{\prime },z)$ be a polynomial that is monic in the complex variable $z$. A Hörmander staircase partitions the real ${\xi }^{\prime }$-space into measurable sets ${\Delta }_j$ and assigns bounded heights $c_j$ so that $P({\xi }^{\prime },s+i{c}_j)$ stays uniformly away from zero for ${\xi }^{\prime }\in {\Delta }_j$ and $s\in \mathbb{R}$. Integrating $1/P$ over the resulting union of horizontal contours constructs a fundamental solution of a linear differential operator.