Chebyshev Polynomials on a System of Continua

2014/04/13 by Andrievskii, V. V.
#30A10 #30C10 #30C62 #30E10 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.3340

Abstract

The estimates of the uniform norm of the Chebyshev polynomial associated with a compact set K consisting of a finite number of continua in the complex plane are established. These estimates are exact (up to a constant factor) in the case where the components of K are either quasismooth (in the sense of Lavrentiev) arcs or closed Jordan domains bounded by a quasismooth curve.

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