Abstract
All those complex Chebyshev polynomials on circular sectors are given explicitly for which the set of extremal points is a certain set E or a subset of E. The case where z n is the Chebyshev polynomial on a circular sector is completely characterized. Some graphs representing the absolute value and the argument of certain selected Chebyshev polynomials on circular sectors are presented, demonstrating in particular the heterogeneous behavior of best complex Chebyshev approximations.
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