论文标题
关于$ q $差异方程的广义电力系列解决方案的收敛
On the convergence of generalized power series solutions of $q$-difference equations
论文作者
论文摘要
提供了足够的条件，可以将广义正式功率系列解决方案与代数$ q $ - 差异方程式收敛。主要结果依靠与此类系列的（复杂）功率指数的半组有关的几何特性。该属性对应于小型分裂现象没有出现的情况。还描述了一些示例说明可以或无法应用足够条件的情况的示例。
A sufficient condition for the convergence of a generalized formal power series solution to an algebraic $q$-difference equation is provided. The main result leans on a geometric property related to the semi-group of (complex) power exponents of such a series. This property corresponds to the situation in which the small divisors phenomenon does not arise. Some examples illustrating the cases where the obtained sufficient condition can be or cannot be applied are also depicted.
