Some results of bernstein and jackson type for polynomial approximation inLp-spaces

  • Alfio Quarteroni

DOI: 10.1007/BF03167866

Cite this article as:
Quarteroni, A. Japan J. Appl. Math. (1984) 1: 173. doi:10.1007/BF03167866


This work is motivated by the analysis of stability and convergence of spectral methods using Chebyshev and Legendre polynomials. We investigate the properties of the polynomial approximation to a functionu in the norms of the weightedLwp (−1, 1) spaces.p is any real number between 1 and ∞, andw(x) is either the Chebyshev or the Legendre weight. The estimates are given in terms of the degreeN of the polynomials and of the smoothness ofu. They include and generalize some theorems of Jackson. Some Bernstein-type inequalities are also given.

Key words

Chebyshev and Legendre approximations Bernstein and Jackson inequalities analysis of spectral methods 

Copyright information

© JJAM Publishing Committee 1984

Authors and Affiliations

  • Alfio Quarteroni
    • 1
  1. 1.Istituto di Analisi Numerica del C.N.R.PaviaItaly

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