g -差分方程的伽罗瓦理论:比较定理

Q4 Mathematics

Confluentes Mathematici Pub Date : 2012-05-08 DOI:10.5802/CML.66

L. D. Vizio, C. Hardouin

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引用次数: 12

摘要

我们建立了$q$差分方程的不同参数化伽罗瓦理论之间的一些比较结果，完成了CHatzidakis, Hardouin和Singer解决无参数情况下问题的工作。我们的主要成果是抽象参数化伽罗瓦理论之间的联系，它给出了$q$-差分方程抽象解的微分性质的信息，以及这类方程的亚纯解的性质。注意，一个具有亚纯系数的线性q -差分方程总是有亚纯解的基，这是由Praagman证明的。

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Galois theories of q-difference equations: comparison theorems

We establish some comparison results among the different parameterized Galois theories for $q$-difference equations, completing the work by CHatzidakis, Hardouin and Singer, that addresses the problem in the case without parameters. Our main result is the link between the abstract parameterized Galois theories, that give information on the differential properties of abstract solutions of $q$-difference equations, and the properties of meromorphic solutions of such equations. Notice that a linear $q$-difference equation with meromorphic coefficients always admits a basis of meromorphic solutions, as proven by Praagman.

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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.