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Direct and Inverse Theorems on Approximation by Piecewise Polynomial Functions

Abstract

The paper is concerned with some characteristics of approximation by piecewise polynomial functions with nonfixed knots in various integral metrics L p [a, b], 0 < p≤∞.

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Correspondence to A. S. Kochurov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 5, pp. 129–144, 2013.

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Kochurov, A.S. Direct and Inverse Theorems on Approximation by Piecewise Polynomial Functions. J Math Sci 209, 96–107 (2015). https://doi.org/10.1007/s10958-015-2487-1

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Keywords

  • Spline Function
  • Hardy Inequality
  • Admissible Function
  • Piecewise Constant Function
  • Hardy Type