Extended Lagrange interpolation on the real line

摘要

Let {pm(wα)}m be the sequence of the polynomials orthonormal w.r.t. the Sonin–Markov weight wα(x)=e−x2|x|α. The authors study extended Lagrange interpolation processes essentially based on the zeros of pm(wα)pm+1(wα), determining the conditions under which the Lebesgue constants, in some weighted uniform spaces, are optimal.