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An application of Szegő polynomials to the computation of certain weighted integrals on the real line

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Abstract

In this paper, a new approach in the estimation of weighted integrals of periodic functions on unbounded intervals of the real line is presented by considering an associated weight function on the unit circle and making use of both Szegő and interpolatory type quadrature formulas. Upper bounds for the estimation of the error are considered along with some examples and applications related to the Rogers-Szegő polynomials, the evaluation of the Weierstrass operator, the Poisson kernel and certain strong Stieltjes weight functions. Several numerical experiments are finally carried out.

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Authors and Affiliations

  1. Department of Mathematical Analysis, La Laguna University, 38271, La Laguna, Tenerife, Canary Islands, Spain

    R. Cruz-Barroso, P. González-Vera & F. Perdomo-Pío

Authors
  1. R. Cruz-Barroso
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  2. P. González-Vera
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  3. F. Perdomo-Pío
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Correspondence to R. Cruz-Barroso.

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Dedicated to Guillermo López-Lagomasino on the occasion of his 60th birthday.

The work of the first author was made during a stay at the Department of Computer Science, Katholieke Universiteit Leuven, and it is partially supported by the Fund of Scientific Research (FWO), project “RAM: Rational modeling: optimal conditioning and stable algorithms”, grant #G.0423.05 and the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attration Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with the author. The work of the third author has been partially supported by a Grant of CajaCanarias and Agencia Canaria de Investigación, Innovación y Sociedad de la Información del Gobierno de Canarias. The work of the three authors is partially supported by Dirección General de Programas y Transferencia de Conocimiento, Ministerio de Ciencia e Innovación of Spain under grant MTM 2008-06671.

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Cruz-Barroso, R., González-Vera, P. & Perdomo-Pío, F. An application of Szegő polynomials to the computation of certain weighted integrals on the real line. Numer Algor 52, 273–293 (2009). https://doi.org/10.1007/s11075-009-9273-4

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