Abstract
Starting from an old result of P. Erdös [1], we give Bernstein and Markov type estimates for the derivative of algebraic and trigonometric polynomials with real zeros. As for the order of magnitude, in some cases these estimates turn out to be optimal.
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References
Erdös, P., On extremal properties of the derivatives of polynomials. Ann. of Math. 41 (1940), 310–313.
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Videnskiǐ, V.S., Extremal estimates for the derivative of a trigonometric polynomial on an interval shorter than the period (Russ.). Dokl. Akad. Nauk SSSR 130 (1) (1960), 13–16.
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© 1981 Birkhäuser Verlag Basel
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Szabados, J. (1981). Bernstein and Markov Type Estimates for the Derivative of a Polynomial with Real Zeros. In: Butzer, P.L., Sz.-Nagy, B., Görlich, E. (eds) Functional Analysis and Approximation. ISNM 60: International Series of Numerical Mathematics / ISNM 60: Internationale Schriftenreihe zur Numerischen Mathematik / ISNM 60: Série internationale d’Analyse numérique, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9369-5_18
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DOI: https://doi.org/10.1007/978-3-0348-9369-5_18
Publisher Name: Birkhäuser Basel
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Online ISBN: 978-3-0348-9369-5
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