D-modules: Local formal convolution of elementary formal meromorphic connections
Robert Gelb
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Robert Gelb, D-modules: Local formal convolution of elementary formal meromorphic connections (2015), Logos Verlag, Berlin, ISBN: 9783832591441
Beschreibung / Abstract
According to the classical theorem of Levelt-Turrittin-Malgrange and its refined version, developed by Claude Sabbah, any meromorphic connection over the field of formal Laurent series in one variable can be decomposed in a direct sum of so called elementary formal meromorphic connections.
Changing the perspective, one can also study operations that can be carried out with such special differential modules. There are already formulas for the tensor product or the local formal Fourier transform, for example.
This thesis analyses the local formal convolution (the multiplicative case as well as the additive case) of two elementary formal meromorphic connections and how the convolution can itself be decomposed into a direct sum of elementary formal meromorphic connections again.
Changing the perspective, one can also study operations that can be carried out with such special differential modules. There are already formulas for the tensor product or the local formal Fourier transform, for example.
This thesis analyses the local formal convolution (the multiplicative case as well as the additive case) of two elementary formal meromorphic connections and how the convolution can itself be decomposed into a direct sum of elementary formal meromorphic connections again.
Inhaltsverzeichnis
- BEGINN
- 1 Introduction
- 2 The nearby cycle functor and its properties
- 3 The multiplicative convolution of elementary mer. connections
- 3.1 Nearby cycle functor and convolution of elementary formal meromorphic connections
- 3.2 A special case
- 3.3 Extension to abitrary meromorphic functions
- 4 The additive convolution of elementary mer. connections
- 4.1 The case m < n
- 4.2 The case n = m
- Appendix