Multidimensional Chebyshev Systems - just a definition

Details Multidimensional Chebyshev Systems - just a definition Multidimensional Chebyshev Systems - just a definition

2008-08-15

arxiv.org/abs/0808.2213v2

Mathematics

Functional Analysis

13 pages

Scientific paper

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.

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