Widom factors

Abstract

Given a non-polar compact set K,we define the n-th Widom factor W<inf>n</inf>(K) as the ratio of the sup-norm of the n-th Chebyshev polynomial on K to the n-th degree of its logarithmic capacity. By G. Szegő, the sequence (Formula presented.) has subexponential growth. Our aim is to consider compact sets with maximal growth of the Widom factors. We show that for each sequence (Formula presented.) of subexponential growth there is a Cantor-type set whose Widom’s factors exceed M<inf>n</inf>. We also present a set K with highly irregular behavior of the Widom factors.