Acta Mathematica Hungarica

, Volume 98, Issue 1, pp 21–30

On a Banach space approximable by Jacobi polynomials

Authors

  • S. P. Yadav
    • Department of Mathematics and Computer ScienceModei Science College Rewa (M.P.)
Article

DOI: 10.1023/A:1022897019476

Cite this article as:
Yadav, S.P. Acta Mathematica Hungarica (2003) 98: 21. doi:10.1023/A:1022897019476

Abstract

Let X represent either the space C[-1,1] Lp(α,β) (w), 1 ≦ p < ∞ on [-1, 1]. Then Xare Banach spaces under the sup or the p norms, respectively. We prove that there exists a normalized Banach subspace X1αβ of Xsuch that every f ∈ X1αβ can be represented by a linear combination of Jacobi polynomials to any degree of accuracy. Our method to prove such an approximation problem is Fourier–Jacobi analysis based on the convergence of Fourier–Jacobi expansions.

Jacobi polynomialBanach spacesapproximation

Copyright information

© Kluwer Academic Publishers/Akadémiai Kiadó 2003