Calculation of local formal Mellin transforms (Q297539)

The local Fourier transform for connections on the punctured formal disk has been studied in papers of H. Bloch, H. Esnault, R. Garcia Lopez, J. Fang, C. Sabbah and D. Arinkin. Local Fourier transforms are shown to induce certain equivalences of categories. In the present paper the author answers a query of Arinkin to prove analogous results about local Mellin transforms. He shows that such transforms induce equivalences between certain categories of vector spaces with connection and vector spaces with invertible difference operators. He finds formulas for explicit calculation in the spirit of the ones performed by Arinkin for local Fourier transforms.