Díaz González, AbelPijeira Cabrera, Héctor EstebanPérez Yzquierdo, Ignacio2022-01-262022-12-012020-12Díaz-González, A., Pijeira-Cabrera, H. & Pérez-Yzquierdo, I. (2020). Rational approximation and Sobolev-type orthogonality. Journal of Approximation Theory, 260, 105481.0021-9045http://hdl.handle.net/10016/33961In this paper, we study the sequence of orthogonal polynomials {Sn}∞ n=0 with respect to the Sobolev-type inner product ⟨ f, g⟩ = ∫ 1 −1 f (x)g(x) dµ(x) + ∑ N j=1 η j f (d j) (c j )g (d j) (c j ) where µ is a finite positive Borel measure whose support supp (µ) ⊂ [−1, 1] contains an infinite set of points, η j > 0, N, d j ∈ Z+ and {c1, . . . , cN } ⊂ R \ [−1, 1]. Under some restriction of order in the discrete part of ⟨·, ·⟩, we prove that for sufficiently large n the zeros of Sn are real, simple, n − N of them lie on (−1, 1) and each of the mass points c j “attracts” one of the remaining N zeros. The sequences of associated polynomials {S [k] n }∞ n=0 are defined for each k ∈ Z+. If µ is in the Nevai class M(0, 1), we prove an analogue of Markov’s Theorem on rational approximation to Markov type functions and prove that convergence takes place with geometric speed.19eng© 2020 Elsevier Inc. All rights reserved.Atribución-NoComercial-SinDerivadas 3.0 EspañaRational approximationSobolev orthogonalityMarkov's theoremZero locationresearch articleMatemáticashttps://doi.org/10.1016/j.jat.2020.105481open access110548119Journal of Approximation Theory260AR/0000027784