Polynomial approximation on $y=x^{\alpha }$
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 | References | Similar Articles | Additional Information
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 $1/{n^{3/2}}$.
- D. J. Newman and L. Raymon, Quantitative polynomial approximation on certain planar sets, Trans. Amer. Math. Soc. 136 (1969), 247–259. MR 234176, DOI https://doi.org/10.1090/S0002-9947-1969-0234176-3
- D. J. Newman, A Müntz-Jackson theorem, Amer. J. Math. 87 (1965), 940–944. MR 186974, DOI https://doi.org/10.2307/2373254 D. J. Newman and E. Passow, An $n$-dimensional Müntz-Jackson theorem, (to appear).
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© Copyright 1970
American Mathematical Society