Multidimensional Chebyshev Systems - just a definition

TL;DR

This paper introduces a new definition for Multidimensional Chebyshev Systems of order N, extending classical one-dimensional systems to a broader class of elliptic equations, addressing a longstanding mathematical challenge.

Contribution

It provides the first satisfactory multidimensional generalization of classical Chebyshev systems, connecting solutions of elliptic equations to these systems.

Findings

Defines Multidimensional Chebyshev Systems of order N

Generalizes classical Chebyshev systems to multiple dimensions

Addresses longstanding problem in mathematical analysis

Abstract

We provide a definition of Multidimensional Chebyshev Systems of order N which is satisfied by the solutions of a wide class of elliptic equations of order 2N. This definition generalizes a very large class of Extended Complete Chebyshev systems in the one-dimensional case. This is the first of a series of papers in this area, which solves the longstanding problem of finding a satisfactory multidimensional generalization of the classical Chebyshev systems introduced already by A. Markov more than hundered years ago, and studied later by S. Bernstein and M. Krein.