Multidimensional Chebyshev Systems - just a definition
For mathematicians working in approximation theory and partial differential equations, this definition offers a long-sought multidimensional generalization of classical Chebyshev systems.
The paper provides a definition of Multidimensional Chebyshev Systems of order N, which generalizes one-dimensional Extended Complete Chebyshev systems and is satisfied by solutions of a wide class of elliptic equations of order 2N, solving a longstanding problem.
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.