Norm estimates for Chebyshev polynomials. II
The behavior of the norms and the so-called Widom factors of Chebyshev polynomials and weighted Chebyshev polynomials on subsets of the unit circle is studied. As subsets, compact subsets are taken that are symmetric with respect to the real line. Upper and lower bounds for the norms in terms of the norms of Chebyshev and weighted Chebyshev polynomials on a certain related subset of \([-1,1]\) are established. In the case of two circular arcs symmetric with respect to the origin, asymptotics of the corresponding Widom factors are derived, as well as exact values of their supremum and infimum are established.
scientific article; zbMATH DE number 7496963
scientific article