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Inequalities for generalized nonnegative polynomials

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Abstract

We define generalized polynomials as products of polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We prove Markov-, Bernstein-, and Remez-type inequalities inL p (0<p<∞) and Nikolskii-type inequalities for such generalized polynomials. Our results extend the corresponding inequalities for ordinary polynomials.

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Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, 43210, Columbus, Ohio, USA

    Tamás Erdélyi & Paul Nevai

  2. Department of Mathematics, Brooklyn College of the City University of New York, 11210, Brooklyn, New York, USA

    Attila Máté

Authors
  1. Tamás Erdélyi
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  2. Attila Máté
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  3. Paul Nevai
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Communicated by George G. Lorentz.

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Erdélyi, T., Máté, A. & Nevai, P. Inequalities for generalized nonnegative polynomials. Constr. Approx 8, 241–255 (1992). https://doi.org/10.1007/BF01238273

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  • DOI: https://doi.org/10.1007/BF01238273

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