Articulos FC INSMAT

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Browsing Articulos FC INSMAT by Author "Ignacio Pérez Yzquierdo"

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    Hessenberg – Sobolev matrices and Favard type theorem
    (2022-12-01) Ignacio Pérez Yzquierdo
    We study the relation between certain non-degenerate lower Hessenberg infinite matrices G and the existence of sequences of orthogonal polynomials with respect to Sobolev inner products. In other words, we extend the well-known Favard theorem for Sobolev orthogonality. We characterize the structure of the matrix G and the associated matrix of formal moments MG in terms of certain matrix operators.
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    Hessenberg –Sobolev Matrices and Favard Type Theorem
    (2022-12-01) Ignacio Pérez Yzquierdo
    We study the relation between certain non-degenerate lower Hessenberg infinite matrices G and the existence of sequences of orthogonal polynomials with respect to Sobolev inner products. In other words, we extend the well-known Favard theorem for Sobolev orthogonality. We characterize the structure of the matrix G and the associated matrix of formal moments MG in terms of certain matrix operators.
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    Rational approximation and Sobolev-type orthogonality
    (2020-12) Ignacio Pérez Yzquierdo
    In this paper, we study the sequence of orthogonal polynomials with respect to the Sobolev-type inner product where is a finite positive Borel measure whose support contains an infinite set of points, and under some restriction of order in the discrete part of , we prove that for sufficiently large the zeros of are real, simple, of them lie on and each of the mass points “attracts” one of the remaining zeros. The sequences of associated polynomials are defined for each. If is in the Nevai class , we prove an analogue of Markov’s Theorem on rational approximation to Markov type functions and prove that convergence takes place with geometric speed.