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The minimality properties of chebyshev polynomials and their lacunary series

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Abstract

By considering four kinds of Chebyshev polynomials, an extended set of (real) results are given for Chebyshev polynomial minimality in suitably weighted Hölder norms on [−1, 1], as well as (L ∞ minimax properties, and bestL 1 sufficiency requirements based on Chebyshev interpolation. Finally we establish bestL p,L ∞ andL 1 approximation by partial sums of lacunary Chebyshev series of the form ∑ ∞1=0 a i ϕ b i(x) whereϕ x (x) is a Chebyshev polynomial andb is an odd integer ≥3. A complete set of proofs is provided.

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Authors and Affiliations

  1. School of Computing and Engineering, University of Huddersfield, HD1 3DH, Queensgate, Huddersfield, UK

    J. C. Mason

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  1. J. C. Mason
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Correspondence to J. C. Mason.

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Mason, J.C. The minimality properties of chebyshev polynomials and their lacunary series. Numer Algor 38, 61–78 (2005). https://doi.org/10.1007/BF02810616

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  • DOI: https://doi.org/10.1007/BF02810616

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