Best Approximations to Polynomials in the Mean and Norms of Coefficient-Functionals

  • Manfred Reimer
Part of the ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique book series (ISNM, volume 51)


A special family of polynomials is investigated by which, on the unit-sphere, the problem of best approximation in the mean to monomials by polynomials of lower degree can be solved. Vice versa, these polynomials are extremal with respect to their leading coefficient. For homogeneous harmonic polynomials, a similar problem can be treated and a bound for the coefficients is obtained, which improves an earlier result of Kellogg essentially.


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Copyright information

© Springer Basel AG 1979

Authors and Affiliations

  • Manfred Reimer
    • 1
  1. 1.Mathematisches InstitutUniversität DortmundDortmund 50W-Germany

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