It is demonstrated by elementary means that the Chebyshev polynomials Tn(z) areoptimal for ellipses in C in a way that extends the classical properties for Tn(x) relative to the real interval [-1, 1].
A theorem of Korovkin states that a sequence of positive linear operators on C[ a, b] converges strongly to the identity if and only if convergence holds on a three-dimensional Chebyshev subspace of C ...
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