Proof of a conjecture of Erdős about the longest polynomial
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- by B. D. Bojanov PDF
- Proc. Amer. Math. Soc. 84 (1982), 99-103 Request permission
Addendum: Proc. Amer. Math. Soc. 89 (1983), 188.
Abstract:
In 1939 P. Erdös conjectured that the Chebyshev polynomial ${T_n}(x)$ has a maximal arc-length in $[ - 1,1]$ among the polynomials of degree $n$ which are bounded by 1 in $[ - 1,1]$. We prove this conjecture for every natural $n$.References
- B. D. Bojanov, An extension of the Markov inequality, J. Approx. Theory 35 (1982), no. 2, 181–190. MR 662166, DOI 10.1016/0021-9045(82)90036-3 P. Erdös, An extremum-problem concerning trigonometric polynomials, Acta Sci. Math. Szeged 9 (1939), 113-115.
- Theodore J. Rivlin, The Chebyshev polynomials, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR 0450850
- J. Szabados, On some extremum problems for polynomials, Approximation and function spaces (Gdańsk, 1979) North-Holland, Amsterdam-New York, 1981, pp. 731–748. MR 649472
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 99-103
- MSC: Primary 41A17
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633287-X
- MathSciNet review: 633287