Summability of formal solutions for some generalized moment partial differential equations

TL;DR

This paper extends moment differentiation to summable functions, providing new summability results for a class of generalized linear moment partial differential equations with variable coefficients.

Contribution

It introduces a framework for moment summability, including integral estimates and path deformations, to analyze solutions of generalized moment PDEs.

Findings

Established summability criteria for solutions of generalized moment PDEs.

Derived upper estimates for integral representations of moment derivatives.

Applied theory to specific classes of equations with variable coefficients.

Abstract

The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment derivatives of functions under exponential-like growth at infinity, and appropriate deformation of the integration paths. The theory is applied to obtain summability results of certain family of generalized linear moment partial differential equations with variable coefficients.