Abstract
AbstractWe consider the Cauchy problem for homogeneous linear q-difference-differential equations with constant coefficients. We characterise convergent, k-summable and multisummable formal power series solutions in terms of analytic continuation properties and growth estimates of the Cauchy data. We also introduce and characterise sequences preserving summability, which make a very useful tool, especially in the context of moment differential equations.
Publisher
Springer Science and Business Media LLC
Reference17 articles.
1. Balser, W.: Moment methods and formal power series. J. Math. Pures Appl. 76, 289–305 (1997)
2. Balser, W.: Formal power series and linear systems of meromorphic ordinary differential equations. Springer-Verlag, New York (2000)
3. Balser, W.: Multisummability of formal power series solutions of partial differential equations with constant coefficients. J. Diff. Equ. 201, 63–74 (2004)
4. Balser, W., Yoshino, M.: Gevrey order of formal power series solutions of inhomogeneous partial differential equations with constant coefficients. Funkcial. Ekvac. 53, 411–434 (2010)
5. Gasper, G., Rahman, M.: Basic Hypergeometric Series. Cambridge University Press, Cambridge (2004)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献