On weighted approximation with Jacobi weights

K. A. Kopotun, D. Leviatan, I. A. Shevchuk

Research output: Contribution to journalArticlepeer-review

Abstract

We obtain matching direct and inverse theorems for the degree of weighted Lp-approximation by polynomials with the Jacobi weights (1−x)α(1+x)β. Combined, the estimates yield a constructive characterization of various smoothness classes of functions via the degree of their approximation by algebraic polynomials. In addition, we prove Whitney type inequalities which are of independent interest.

Original languageEnglish
Pages (from-to)96-112
Number of pages17
JournalJournal of Approximation Theory
Volume237
DOIs
StatePublished - Jan 2019

Keywords

  • Approximation by polynomials in weighted L-norms
  • Characterization of smoothness classes
  • Degree of approximation
  • Direct and inverse theorems
  • Jacobi weights
  • Moduli of smoothness
  • Whitney-type estimates

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