Markov's Theorem for Sobolev-type inner product sequentially-ordered

by Abel Díaz González (Universidad Carlos III de Madrid)

Location: 200B.02.18, Leuven
Time: Wednesday March 13, 2019 at 10:30

We study the sequence of orthogonal polynomials {S_n} with respect to a discrete Sobolev inner product whose measure is supported in [-1,1] and belongs to the Nevai class. Under some restriction of order in the discrete part, we prove that for n sufficiently large the zeros of S_n are real, simple, n-N of them lie on (-1,1) and each of the mass points “attracts” one of the remaining N zeros, where N denotes the number of mass point in the discrete part. The sequences of associated polynomials are defined. We prove an analog of the Markov’s theorem on rational approximation of some class holomorphic functions and we give an estimate of the “speed” of convergence.