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Mean oscillation modulus and number-theoretic grid quadrature formulas

  • Volume 101, Number 2, February, 2017
  • Published:
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Abstract

For arbitrary Riemann integrable functions f and irrational numbers θ ∈ (0, 1), we obtain estimates of the error R n (f, θ) of the quadrature formula

$$\int_0^1 {f\left( x \right)dx = \frac{1}{n}\sum\limits_{k = 1}^n {f\left( {\left\{ {k\theta } \right\}} \right) - {R_n}\left( {f,\theta } \right)} } $$

in which {kθ} is the fractional part of the number kθ.

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Authors and Affiliations

  1. National Research Nuclear University “MIFI,”, Moscow, Russia

    E. A. Sevast’yanov

Authors
  1. E. A. Sevast’yanov
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Correspondence to E. A. Sevast’yanov.

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Original Russian Text © E. A. Sevast’yanov, 2017, published in Matematicheskie Zametki, 2017, Vol. 101, No. 2, pp. 262–285.

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Sevast’yanov, E.A. Mean oscillation modulus and number-theoretic grid quadrature formulas. Math Notes 101, 320–340 (2017). https://doi.org/10.1134/S0001434617010369

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