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...

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Detalles Bibliográficos
Autores: Gontsov, Renat, Goryuchkina, Irina, Lastra Sedano, Alberto|||0000-0002-4012-6471
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
Descripción
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.