On the Lebesgue constant for the Xu interpolation formula

In the paper [8], the author introduced a set of Chebyshev-like points for polynomial interpolation (by a certain subspace of polynomials) in the square [−1, 1], and derived a compact form of the corresponding Lagrange interpolation formula. In [1] we gave an efficient implementation of the Xu interpolation formula and we studied numerically its Lebesgue constant, giving evidence that it grows like O((log n)), n being the degree. The aim of the present paper is to provide an analytic proof that indeed the Lebesgue constant does have this order of growth.