Polynomial approximation in Lp (0<p<1)

Ronald A. DeVore, Dany Leviatan, Xiang Ming Yu

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that for f∈Lp, 0<p<1, and k a positive integer, there exists an algebraic polynomial Pn of degree ≤n such that {Mathematical expression} where ωkφ{symbol}(f, t)p is the Ditzian-Totik modulus of smoothness of f in Lp, and C is a constant depending only on k and p. Moreover, if f is nondecreasing and k≤2, then the polynomial Pn can also be taken to be nondecreasing.

Original languageEnglish
Pages (from-to)187-201
Number of pages15
JournalConstructive Approximation
Volume8
Issue number2
DOIs
StatePublished - Jun 1992

Keywords

  • AMS classification: 41A25, 41A20
  • Degree of approximation
  • Monotone approximation
  • Polynomials

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