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Polynomial approximation on $ y=x\sp{\alpha }$


Authors: E. Passow and L. Raymon
Journal: Proc. Amer. Math. Soc. 24 (1970), 781-783
MSC: Primary 41.41
DOI: https://doi.org/10.1090/S0002-9939-1970-0257624-5
MathSciNet review: 0257624
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Abstract: We show that on the curve $ y = {x^\alpha },\alpha $ any irrational, $ 0 \leqq x \leqq 1$, the degree of approximation by $ n$th degree polynomials in $ x$ and $ y$ in the $ {L^2}$ norm has order of magnitude $ 1/{n^{3/2}}$.


References [Enhancements On Off] (What's this?)

  • [1] D. J. Newman and L. Raymon, Quantitative polynomial approximation on certain planar sets, Trans. Amer. Math. Soc. 136 (1969), 247-259. MR 38 #2494. MR 0234176 (38:2494)
  • [2] D. J. Newman, A Müntz-Jackson theorem, Amer. J. Math. 87 (1965), 940-944. MR 32 #4429. MR 0186974 (32:4429)
  • [3] D. J. Newman and E. Passow, An $ n$-dimensional Müntz-Jackson theorem, (to appear).

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DOI: https://doi.org/10.1090/S0002-9939-1970-0257624-5
Article copyright: © Copyright 1970 American Mathematical Society

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