Estimates of formal solutions for some generalized moment partial differential equations

Abstract

Using increasing sequences of real numbers, we generalize the idea of formal moment differentiation first introduced by W. Balser and M. Yoshino. Slight departure from the concept of Gevrey sequences enables us to include a wide variety of operators in our study. Basing our approach on tools such as the Newton polygon and divergent formal norms, we obtain estimates for formal solutions of certain families of generalized linear moment partial differential equations with constant and time variable coefficients.

arXiv comment16 pages

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Cited by in corpus (4)

• Summability of formal solutions for a family of generalized moment integro-differential equations
• Multisummability of formal solutions for a family of generalized singularly perturbed moment differential equations
• On the summability and convergence of formal solutions of linear $q$-difference-differential equations with constant coefficients
• On integral representations of $q$-difference operators and their applications