D-Modules: Local Formal Convolution of Elementary Formal Meromorphic Connections (Paperback) (ISBN-13: 9783832538941)

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.

Author: Robert Gelb
ISBN-10: 3832538941
ISBN-13: 9783832538941
Publisher: Logos Verlag Berlin
Language: English
Published: 02/28/2015
Pages: 95
Format: Paperback