Bernstein–Walsh Inequalities in Higher Dimensions over Exponential Curves

Shirali Kadyrov, Mark Lawrence

    Research output: Contribution to journal › Article

    1 Citation (Scopus)

    Abstract

    Let (Formula presented.) be linearly independent over (Formula presented.), and set (Formula presented.) We prove sharp estimates for the growth of a polynomial of degree n, in terms of (Formula presented.)where (Formula presented.) is the unit polydisk. For all (Formula presented.) with linearly independent entries, we have the lower estimate (Formula presented.)for Diophantine (Formula presented.), we have (Formula presented.)In particular, this estimate holds for almost all (Formula presented.) with respect to Lebesgue measure. The results here generalize those of Coman and Poletsky [6] for (Formula presented.) without relying on estimates for best approximants of rational numbers which do not hold in the vector-valued setting.

    Original languageEnglish
    JournalConstructive Approximation
    DOIs
    Publication statusAccepted/In press - Oct 26 2015

    Fingerprint

    Higher Dimensions
    Polynomials
    Curve
    Estimate
    Linearly
    Polydisk
    Order of a polynomial
    Lebesgue Measure
    Generalise
    Unit

    Keywords

    • Bernstein–Walsh inequalities
    • Hausdorff dimension
    • Liouville vectors
    • Polynomial inequalities

    ASJC Scopus subject areas

    • Mathematics(all)
    • Analysis
    • Computational Mathematics

    Cite this

    Bernstein–Walsh Inequalities in Higher Dimensions over Exponential Curves. / Kadyrov, Shirali; Lawrence, Mark.

    In: Constructive Approximation, 26.10.2015.

    Research output: Contribution to journal › Article

    Kadyrov, S & Lawrence, M 2015, 'Bernstein–Walsh Inequalities in Higher Dimensions over Exponential Curves', Constructive Approximation. https://doi.org/10.1007/s00365-015-9314-2
    Kadyrov S, Lawrence M. Bernstein–Walsh Inequalities in Higher Dimensions over Exponential Curves. Constructive Approximation. 2015 Oct 26. https://doi.org/10.1007/s00365-015-9314-2
    Kadyrov, Shirali ; Lawrence, Mark. / Bernstein–Walsh Inequalities in Higher Dimensions over Exponential Curves. In: Constructive Approximation. 2015.
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