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On the summability and convergence of formal solutions of linear $q$-difference-differential equations with constant coefficients (2301.10331v2)
Published 24 Jan 2023 in math.AP, math.CA, and math.CV
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.