CONTRIBUTIONS TO RATIONAL APPROXIMATION,

Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haars linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev approximation are obtained. These results include a topological description of the continuous functions at which the Chebyshev operator is continuous. Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. Author