On the summability and convergence of formal solutions of linear $q$-difference-differential equations with constant coefficients

Abstract

We 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.

22 pages

References in corpus (4)

• Summability of formal solutions of linear partial differential equations with divergent initial data
• Analytic and summable solutions of inhomogeneous moment partial differential equations
• Estimates of formal solutions for some generalized moment partial differential equations
• Summable solutions of the Goursat problem for some partial differential equations with constant coefficients

Cited by in corpus (1)

• On sequences preserving summability