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On Chebyshev polynomials in the complex plane

Published 22 Jan 2017 in math.CV | (1701.06202v1)

Abstract: The estimates of the uniform norm of the Chebyshev polynomials associated with a compact set $K$ in the complex plane are established. These estimates are exact (up to a constant factor) in the case where $K$ consists of a finite number of quasiconformal curves or arcs. The case where $K$ is a uniformly perfect subset of the real line is also studied.

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