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A commutation theorem on Mellin transform on sheaves and the functor of solutions

Herve Fabbro
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Abstract

We describe the complex of solutions of the algebraic Mellin transform of a $\mathcal{D}$-module $\mathcal{M}$ in terms of the solutions of $\mathcal{M}$. In order to do that, we define a Mellin functor on sheaves. We show the Mellin transform of the complex of rapid decay solutions of a regular holonomic $\mathcal{D}$-module $\mathcal{M}$ is quasi-isomorphic to the complex of solutions of the algebraic Mellin transform of $\mathcal{M}$, the assumption of regularity not being necessary in the one variable case.

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Herve Fabbro. 2007-02-08. A commutation theorem on Mellin transform on sheaves and the functor of solutions. https://arxiv.org/abs/math/0702229

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