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Characterization of the speed of convergence of the trapezoidal rule

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Summary

Our aim is to determine the precise space of functions for which the trapezoidal rule converges with a prescribed rate as the number of nodes tends to infinity. Excluding or controlling odd functions in some way it is possible to establish a correspondence between the speed of convergence and regularity properties of the function to be integrated. In this way we characterize Sobolev spaces, certain spaces of infinitely differentiable functions, of functions holomorphic in a strip, of entire functions of order greater than 1 and of entire functions of exponential type by the speed of convergence.

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Authors and Affiliations

  1. Départment de mathématiques et de statistique, Université de Montréal, H3C 3J7, Montréal, Québec, Canada

    Qazi I. Rahman

  2. Mathematisches Institut, Universität Erlangen-Nürnberg, D-8520, Erlangen, Federal Republic of Germany

    Gerhard Schmeisser

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  1. Qazi I. Rahman
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  2. Gerhard Schmeisser
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Dedicated to Professor G. Hämmerlin on the occasion of his 60th birthday

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Rahman, Q.I., Schmeisser, G. Characterization of the speed of convergence of the trapezoidal rule. Numer. Math. 57, 123–138 (1990). https://doi.org/10.1007/BF01386402

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