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

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

2007-02-08

arxiv.org/abs/math/0702229v1

Mathematics

Algebraic Geometry

22 pages, LaTeX document

Scientific paper

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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