Let $U \subset \mathbb{R}^n$ be open, let $m \in \mathbb{R}$, and let
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\begin{align*}
a_{m-j}: U \times (\mathbb{R}^n \setminus \{0\}) \to \mathbb{C}
\end{align*}
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be a smooth function for each $j \in \mathbb{N} \cup \{0\}$. Assume that each $a_{m-j}$ is positively homogeneous of degree $m-j$ in the covariable, meaning that