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On a Banach space approximable by Jacobi polynomials

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Abstract

Let X represent either the space C[-1,1] L p (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 X 1 αβ of Xsuch 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.

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  1. Department of Mathematics and Computer Science, Modei Science College Rewa (M.P.), 486 001, India

    S. P. Yadav

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  1. S. P. Yadav
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Yadav, S.P. On a Banach space approximable by Jacobi polynomials. Acta Mathematica Hungarica 98, 21–30 (2003). https://doi.org/10.1023/A:1022897019476

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