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A relation between spline approximation and the problem of the approximation of one class by another

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Abstract

An investigation of the approximation in Lq(−∞, ∞) of differentiable functions whose k-th derivatives belong to Lp(−∞, ∞), by splines Sm (x) with nonfixed nodes, under the extra assumption that the norms in Ls(−∞, ∞) of theirl-th derivatives have a common bound. A relation is established with the problem of approximating functions of one class by functions of another class.

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Literature cited

  1. V. V. Arestov and V. N. Gabushin, “The approximation of classes of differentiable functions,” Matem. Zametki,9, No. 2, 105–112 (1971).

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  2. Yu. N. Subbotin and N. I. Chernykh, “The order of best spline approximations for certain classes of functions,” Matem. Zametki,7, No. 1, 31–42 (1970).

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  3. Yu. N. Subbotin, “The diameter of the class WrL in L (0, 2π) and the approximation by splines,” Matem. Zametki,7, No. 1, 43–52 (1970).

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Authors and Affiliations

  1. V. A. Steklov Mathematics Institute, Sverdlovsk Branch, Academy of Sciences of the USSR, USSR

    Yu. No Subbotin

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  1. Yu. No Subbotin
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Translated from Matematicheskie Zametki, Vol. 9, No. 5, pp. 501–510, May, 1971.

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Subbotin, Y.N. A relation between spline approximation and the problem of the approximation of one class by another. Mathematical Notes of the Academy of Sciences of the USSR 9, 289–294 (1971). https://doi.org/10.1007/BF01094354

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  • DOI: https://doi.org/10.1007/BF01094354

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