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 function u in the norms of the weighted Lwp (-1, 1) spaces. p is any real number between 1 and ∞, and w(x) is either the Chebyshev or the Legendre weight. The estimates are given in terms of the degree N of the polynomials and of the smoothness of u. They include and generalize some theorems of Jackson. Some Bernstein-type inequalities are also given. © 1984 JJAM Publishing Committee.

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

QUARTERONI, ALFIO MARIA
1984

Abstract

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 function u in the norms of the weighted Lwp (-1, 1) spaces. p is any real number between 1 and ∞, and w(x) is either the Chebyshev or the Legendre weight. The estimates are given in terms of the degree N of the polynomials and of the smoothness of u. They include and generalize some theorems of Jackson. Some Bernstein-type inequalities are also given. © 1984 JJAM Publishing Committee.
analysis of spectral methods, Bernstein and Jackson inequalities, Chebyshev and Legendre approximations
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/669765
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