Multidimensional Chebyshev Systems - just a definition

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. 1 History of Chebyshev systems 1.1 Developments in the Moment problem by A. Markov and M. Krein It was namely in the Moment problem where the Chebyshev systems appeared for the first time on the big stage, and provided a very natural and beautiful generalizations of the results of Gauss, Jacobi, Chebyshev, Stieltjes and Markov, and others. The classical Moment problem is defined as follows: Find a non-negative measure dμ such that