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Convex functions and Fourier coefficients

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Abstract

The aim of this paper is to prove that the cosine Fourier coefficients \(a_{mn}\) (with \(m,n\ge 1)\) of a Popoviciu convex function of two variables are nonnegative.

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Acknowledgements

The authors are greatly indebted to Sorin G. Gal for several suggestions which have improved the final version of this paper.

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Correspondence to Constantin P. Niculescu.

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Niculescu, C.P., Rovenţa, I. Convex functions and Fourier coefficients. Positivity 24, 129–139 (2020). https://doi.org/10.1007/s11117-019-00670-8

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Keywords

  • Fourier coefficients
  • Divided double difference
  • 2d-Monotonicity
  • Popoviciu convex function

Mathematics Subject Classification

  • Primary 26B25
  • 42B05
  • Secondary 26D05