On the convergence of generalized power series solutions of q-difference equations

被引：0
|
作者：
Renat Gontsov
Irina Goryuchkina
Alberto Lastra
机构：
[1] Institute for Information Transmission Problems of the Russian Academy of Sciences,Keldysh Institute of Applied Mathematics
[2] Russian Academy of Sciences,undefined
[3] Universidad de Alcalá Departamento de Física y Matemáticas,undefined
来源：
Aequationes mathematicae | 2022年 / 96卷
关键词：
Convergence; Generalized formal power series; -difference equation; 39A13 (Primary); 39A45 (Secondary);
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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 or cannot be applied are also depicted.
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页码：579 / 597
页数：18
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