Rational approximation and Sobolev-type orthogonality
Rational approximation and Sobolev-type orthogonality
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Date
2020-12
Authors
Ignacio Pérez Yzquierdo
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Abstract
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.
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Pérez Yzquierdo, I. (2020). Rational approximation and Sobolev-type orthogonality. Journal of Approximation Theory, 260, 105481.