Chebyshev Polynomials on a System of Continua

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.