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The error norm of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegö type

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Abstract

We consider the Gauss-Kronrod quadrature formulae for the Bernstein-Szegö weight functions consisting of any one of the four Chebyshev weights divided by the polynomial On certain spaces of analytic functions, the error term of these formulae is a continuous linear functional. We compute explicitly the norm of the error functional.

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  1. Department of Mathematics, University of Athens, Panepistemiopolis, 15784, Athens, Greece

    Sotirios E. Notaris

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  1. Sotirios E. Notaris
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Correspondence to Sotirios E. Notaris.

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Work supported in part by a grant from the Research Committee of the University of Athens, Greece, and in part by a ``Pythagoras'' O.P. Education grant to the University of Athens from the Ministry of National Education, Greece, and the European Union.

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Notaris, S. The error norm of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegö type. Numer. Math. 103, 99–127 (2006). https://doi.org/10.1007/s00211-005-0670-x

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  • DOI: https://doi.org/10.1007/s00211-005-0670-x

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