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Orthogonal Polynomials of Discrete Variable and Boundedness of Dirichlet Kernel

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Constructive Approximation Aims and scope

Abstract

For orthogonal polynomials defined by compact Jacobi matrix with exponential decay of the coefficients, precise properties of orthogonality measure is determined. This allows showing uniform boundedness of partial sums of orthogonal expansions with respect to L∞ norm, which generalize analogous results obtained, for little q-Legendre, little q-Jacobi, and little q-Laguerre polynomials, by the authors.

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Authors and Affiliations

  1. Institute of Biomathematics and Biometry, GSF-National Research Center for Environment and Health, Ingolstadter Landstrasse 1, D-85764, Neuherberg, Germany

    Josef Obermaier

  2. Institute of Mathematics, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384, Wroclaw, Poland

    Ryszard Szwarc

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  1. Josef Obermaier
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  2. Ryszard Szwarc
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Correspondence to Josef Obermaier or Ryszard Szwarc.

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Obermaier, J., Szwarc, R. Orthogonal Polynomials of Discrete Variable and Boundedness of Dirichlet Kernel. Constr Approx 27, 1–13 (2008). https://doi.org/10.1007/s00365-006-0645-4

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  • DOI: https://doi.org/10.1007/s00365-006-0645-4

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