On the convergence of generalized power series solutions of q-difference equations
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/50571DOI: 10.1007/s00010-021-00817-7
ISSN: 0001-9054
Publisher
Springer Nature
Date
2021-06-01Embargo end date
2022-06-01Funders
Agencia Estatal de Investigación
Universidad de Alcalá
Bibliographic citation
Gontsov, R., Goryuchkina, I. & Lastra, A. 2021, “On the convergence of generalized power series solutions of q-difference equations”, Aequationes mathematicae (2021), https://doi.org/10.1007/s00010-021-00817-7
Keywords
Convergence
Generalized formal power series
q-difference equation
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105621GB-I00/ES/METODOS ASINTOTICOS, ALGEBRAICOS Y GEOMETRICOS EN FOLIACIONES SINGULARES Y SISTEMAS DINAMICOS/
info:eu-repo/grantAgreement/UAH//CM-JIN-2019-010
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1007/s00010-021-00817-7Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2021 the autors, under the exclusive licence to Springer Nature
Access rights
info:eu-repo/semantics/openAccess
Abstract
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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