On a Banach space approximable by Jacobi polynomials 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] L _{p} ^{(α,β)} (w), 1 ≦ p < ∞ on [-1, 1]. Then X are Banach spaces under the sup or the p norms, respectively. We prove that there exists a normalized Banach subspace X ^{1} _{αβ} of X such that every f ∈ X ^{1} _{αβ} 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 polynomial Banach spaces approximation

This revised version was published online in June 2006 with corrections to the Cover Date.

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Authors and Affiliations 1. Department of Mathematics and Computer Science Modei Science College Rewa (M.P.) India