On the convergence of generalized power series solutions of q-difference equations
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 situatio...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/50571 |
| Acceso en línea: | http://hdl.handle.net/10017/50571 https://dx.doi.org/10.1007/s00010-021-00817-7 |
| Access Level: | acceso abierto |
| Palabra clave: | Convergence Generalized formal power series q-difference equation Matemáticas Mathematics |
| Sumario: | 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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