On Mason's conjecture concerning interpolation by polynomials in z and z-1 on an annulus

A polynomial of degree n in z^–1 and n – 1 in z isdefined by an interpolation projection from the space A(N) of functions f analytic in thecircular annulus ^–1<|z| and continuous on its boundaries|z|=^–1, . The points of interpolation are chosen to coincidewith the n roots of zⁿ=–n and the n roots of zⁿ=^–n.We prove Mason's conjecture that the corresponding Lebesguefunction attains its maximal value on the inner circle. We alsoestimate the bound of the Lebesgue constant . It is proved that the following estimate for theoperator norm holds: where _n, is the Lebesgue constant of Gronwall for equally spacedinterpolation on a circle by a polynomial of degree n.