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On the best approximation of functions ofn variables

Abstract

We propose a new approach to the solution of the problem of the best approximation, by a certain subspace for functions ofn variables determined by restrictions imposed on the modulus of, continuity of certain partial derivatives. This approach is based on the duality theorem and on the representation of a function as a countable sum of simple functions.

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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 10, pp. 1352–1359, October, 1999.

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Korneichuk, N.P. On the best approximation of functions ofn variables. Ukr Math J 51, 1525–1533 (1999). https://doi.org/10.1007/BF02981685

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Keywords

  • Periodic Function
  • Normed Space
  • Simple Function
  • Trigonometric Polynomial
  • Duality Theorem