Annihilators of Laurent coefficients of the complex power for normal crossing singularity

Let $f$ be a real-valued real analytic function defined on an open set of $\mathbb{R}^n$. Then the complex power $f_+^λ$ is defined as a distribution with a holomorphic parameter $λ$. We determine the annihilator (in the ring of differential operators) of each coefficient of the principal part of the Laurent expansion of $f_+^λ$ about $λ=-1$ in case $f=0$ has a normal crossing singularity.

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