Calculation of local formal Mellin transforms
Calculation of local formal Mellin transforms
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局部正式 Mellin 变换的计算
DOI：
10.2140/pjm.2016.283.115
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Adam Graham
中科院分区：
文献类型：
--
作者：
Adam Graham
最近的许多工作已经做了局部傅立叶变换的连接上的穿孔正式磁盘。具体来说，局部傅立叶变换已被引入，诱导某些等价的类别，并已发现明确的公式来计算它们。在本文中，我们证明了类似的结果，在类似的情况下，局部梅林变换的联络上的穿孔正式磁盘。具体来说，我们介绍了当地梅林变换，并表明，他们诱导某些类别的向量空间与连接和向量空间与可逆差分算子之间的等价性，以及找到公式明确的计算在相同的精神，计算当地傅立叶变换。
Much recent work has been done on the local Fourier transforms for connections on the punctured formal disk. Specifically, the local Fourier transforms have been introduced, shown to induce certain equivalences of categories, and explicit formulas have been found to calculate them. In this paper, we prove analogous results in a similar situation, the local Mellin transforms for connections on the punctured formal disk. Specifically, we introduce the local Mellin transforms and show that they induce equivalences between certain categories of vector spaces with connection and vector spaces with invertible difference operators, as well as find formulas for explicit calculation in the same spirit as the calculations for the local Fourier transforms.