Polynomial interpolation, an L-function, and pointwise approximation of continuous functions

• Autores: Michael I. Ganzburg
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 153, Nº 1, 2008, págs. 1-18
• Idioma: inglés
• DOI: 10.1016/j.jat.2006.09.008
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• Resumen

  • We show that if is the sequence of all zeros of the L-function satisfying then any function from span satisfies the pointwise rapid convergence property, i.e. there exists a sequence of polynomials Qn(f,x) of degree at most n such that and for every x[-1,1],limn?8(f(x)-Qn(f,x))/En(f)=0, where En(f) is the error of best polynomial approximation of f in C[-1,1]. The proof is based on Lagrange polynomial interpolation to xs, , at the Chebyshev nodes. We also establish a new representation for L(x,?).