Estimates for the Lorentz degree of polynomials. (English) Zbl 0759.41003
The author establishes lower bounds for the Lorentz degree of certain special polynomials.
Reviewer: M.A.Ibiejugba (Ilorin)
MSC:
| 41A10 | Approximation by polynomials |
Keywords:
Lorentz degreeReferences:
| [1] | Bernstein, S. N., Sur la représentation des polynomes positifs, (Constructive Theory of Functions (1905-1930). Constructive Theory of Functions (1905-1930), Collected Papers of S. N. Bernstein, Vol. 1 (1952), Academy of Sciences: Academy of Sciences USSR), 251-252, [in Russian; the original paper was published in 1915] · JFM 48.1371.04 |
| [2] | Erdélyi, T., Markov-type inequalities for trigonometric polynomials of special type, Acta Math. Hungar., 51, Nos. 3-4, 421-436 (1988) · Zbl 0659.42002 |
| [3] | Erdélyi, T., Markov and Bernstein type inequalities for certain classes of constrained trigonometric polynomials on an interval shorter than the period, Studia Sci. Math. Hungar., 25, Nos. 1-2, 3-25 (1990) · Zbl 0628.41014 |
| [4] | Erdélyi, T.; Szabados, J., On polynomials with positive coefficients, J. Approx. Theory, 54, 107-122 (1988) · Zbl 0653.41010 |
| [5] | Erdélyi, T.; Szabados, J., On trigonometric polynomials with positive coefficients, Studia Sci. Math. Hungar., 24, No. 1, 71-91 (1989) · Zbl 0676.42003 |
| [6] | Erdélyi, T.; Szabados, J., Bernstein-type inequalities for a class of polynomials, Acta Math. Hungar., 53, Nos. 1-2, 237-251 (1989) · Zbl 0731.42001 |
| [7] | Ferguson, B. O., Approximation by polynomials with integral coefficients, (Math. Surveys No. 17 (1980), Amer. Math. Soc: Amer. Math. Soc Providence, RI) · Zbl 0213.08702 |
| [8] | Lorentz, G. G., Bernstein Polynomials (1953), Toronto Univ. Press: Toronto Univ. Press Toronto · Zbl 0051.05001 |
| [9] | Lorentz, G. G., The degree of approximation by polynomials with positive coefficients, Math. Ann., 151, 239-251 (1963) · Zbl 0116.04602 |
| [11] | Saff, E. B., Incomplete and orthogonal polynomials, (Chui, C. K.; Schumaker, L. L.; Ward, J. D., Approximation Theory IV (1983), Academic Press: Academic Press New York), 219-256 · Zbl 0563.41006 |
| [12] | Saff, E. B.; Varga, R. S., On incomplete polynomials, (Collatz, L.; etal., Numerischen Methoden der Approximationstheorie. Numerischen Methoden der Approximationstheorie, I.S.N.M., Vol. 42 (1978), Birkhäuser: Birkhäuser Basel), 281-298, Vol. 4 · Zbl 0424.41004 |
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