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On the accuracy of cubature formulas in Sobolev spaces

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Abstract

We establish the necessary and sufficient conditions for the boundedness of the cubature formulas error functionals in spaces of type L m p corresponding to the considered sets of integrable functions defined on bounded subsets of cylindrical and conical surfaces.

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Authors and Affiliations

  1. Siberian Federal University, Krasnoyarsk, 660041, Russia

    V. I. Polovinkin

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  1. V. I. Polovinkin
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Correspondence to V. I. Polovinkin.

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Original Russian Text © V. I. Polovinkin, 2009, published in Journal of Siberian Federal University, 2009, Vol. 1, No. 2, pp. 59–68.

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Polovinkin, V.I. On the accuracy of cubature formulas in Sobolev spaces. Sib. Adv. Math. 22, 41–49 (2012). https://doi.org/10.3103/S1055134412010038

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  • DOI: https://doi.org/10.3103/S1055134412010038

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