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Rational Approximation and Interpolation pp 125–135Cite as

Bernstein and markov inequalities for constrained polynomials

  • Approximation And Interpolation Theory
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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1105))

Abstract

Pointwise and uniform bounds are determined for the derivatives of real algebraic polynomials p(x) which on the interval [−1,1] satisfy (1−x2)λ/2|p(x)| ≤ 1, λ a fixed positive integer. The pointwise bounds are investigated with regard to their sharpness while the uniform bounds are shown to be best possible in an asymptotic sense.

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References

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan-Dearborn, 48128, Dearborn, Michigan, USA

    Michael A. Lachance

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  1. Michael A. Lachance
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Peter Russell Graves-Morris Edward B. Saff Richard S. Varga

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© 1984 Springer-Verlag

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Lachance, M.A. (1984). Bernstein and markov inequalities for constrained polynomials. In: Graves-Morris, P.R., Saff, E.B., Varga, R.S. (eds) Rational Approximation and Interpolation. Lecture Notes in Mathematics, vol 1105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072405

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  • DOI: https://doi.org/10.1007/BFb0072405

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13899-0

  • Online ISBN: 978-3-540-39113-5

  • eBook Packages: Springer Book Archive

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