Abstract
We study the order (velocity) of the approximation of functions on the axis by entire functions of exponential type not higher than σ as σ → ∞ (the linear and best approximations). The exact order of approximation of individual functions on ℝd by the classical summation methods of Fourier integrals (Gauss–Weierstrass, Bochner–Riesz, Marcinkiewicz) and the nonclassical Bernstein–Stechkin method is found. For functions on a torus, similar theorems of approximation by polynomials were obtained previously.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 12, No. 2, pp. 222–242, April–May, 2015.
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Kotova, O.V., Trigub, R.M. Approximative properties of the summation methods of Fourier integrals. J Math Sci 211, 668–683 (2015). https://doi.org/10.1007/s10958-015-2623-y
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DOI: https://doi.org/10.1007/s10958-015-2623-y