In Mebkhout's paper on Local Cohomology of Analytic Spaces, the following theorem is stated:
Let $X$ be a complex smooth manifold and $Y$ is an analytic subspace of $X$. Then $\mathcal{D}_X^{\infty}\otimes_{\mathcal{D}_X}R\Gamma_{[Y]}(\mathcal{O}_X) \simeq R\Gamma_Y(\mathcal{O}_X)$ is an isomorphism in the derived category of $\mathcal{D}_X^{\infty}$ modules. Moreover, the local cohomology sheaves of $Y$ are $\mathcal{D}_X^{\infty}$ holonomic and admissible.
My understanding is that $\mathcal{D}_X^{\infty}$ is the restriction of $\mathcal{E}_X^{\infty}$ to the zero section of the cotangent bundle of $X$. Is it correct? What does it mean by "holonomic" and "admissible" in this $\mathcal{D}_X^{\infty}$ category? Could anyone kindly point to some references?
Thanks!
