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Orthogonal Algebraic Polynomial Schauder Bases of Optimal Degree

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Abstract

For any fixed \(\varepsilon > 0\) we construct an orthonormal Schauder basis \(\{p_\mu\}_{\mu=0}^{\infty}\) for C[-1,1] consisting of algebraic polynomials \(p_\mu\) with \(\deg p_\mu \le (1+\varepsilon) \mu .\) The orthogonality is with respect to the Chebyshev weight.

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Authors and Affiliations

  1. Mathematics, Auburn University, Auburn, Alabama 36849, USA

    T. Kilgore

  2. FB Mathematik, Universitat Rostock, D-18051 Rostock, Germany

    J. Prestin & K. Selig

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  1. T. Kilgore
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  2. J. Prestin
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  3. K. Selig
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Kilgore, T., Prestin, J. & Selig, K. Orthogonal Algebraic Polynomial Schauder Bases of Optimal Degree. J Fourier Anal Appl 2, 597–610 (1995). https://doi.org/10.1007/s00041-001-4045-0

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  • DOI: https://doi.org/10.1007/s00041-001-4045-0

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