Entire solutions of linear systems of moment differential equations and related asymptotic growth at infinity

TL;DR

This paper characterizes entire solutions of linear moment differential systems using moment kernels and Jordan decomposition, and analyzes their asymptotic growth at infinity in various directions.

Contribution

It provides a comprehensive description of entire solutions via moment kernels and Jordan form, and determines their growth behavior at infinity.

Findings

Solutions are expressed through moment kernel functions and Jordan decomposition.

The growth order and type of solutions are explicitly determined.

Asymptotic behavior of solutions along rays to infinity is characterized.

Abstract

The general entire solution to a linear system of moment differential equations is obtained in terms of a moment kernel function for generalized summability, and the Jordan decomposition of the matrix defining the problem. The growth at infinity of any solution of the system is also determined, both globally and also following rays to infinity, determining the order and type of such solutions.