Multidimensional Version of Lagrange's Problem on Mean Motion

TL;DR

This paper extends Lagrange's mean motion problem, originally proven for exponential polynomials in one dimension, to a multidimensional setting, establishing the existence of an average speed for amplitudes in higher dimensions.

Contribution

It provides the first multidimensional generalization of Lagrange's mean motion problem, expanding the scope of the original theorem to multiple variables.

Findings

Proved the multidimensional version of Lagrange's problem.

Established the existence of average amplitude speed in higher dimensions.

Extended classical results to a broader mathematical context.

Abstract

The famous mean motion problem which goes back to Lagrange as follows: to prove that any exponential polynomial with exponents on the imaginary axis has an average speed for the amplitude, whenever the variable moves along a horizontal line. It was completely proved by B. Jessen and H. Tornehave in Acta Math.77, 1945. Here we give its multidimensional version.