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Subperiodic Dubiner distance, norming meshes and trigonometric polynomial optimization

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Abstract

We extend the notion of Dubiner distance from algebraic to trigonometric polynomials on subintervals of the period, and we obtain its explicit form by the Szegő variant of Videnskii inequality. This allows to improve previous estimates for Chebyshev-like trigonometric norming meshes, and suggests a possible use of such meshes in the framework of multivariate polynomial optimization on regions defined by circular arcs.

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Acknowledgements

Work partially supported by the Horizon 2020 ERA-PLANET European project “GEOEssential”, by the DOR funds and the biennial Project BIRD163015 of the University of Padova, and by the GNCS-INdAM. This research has been accomplished within the RITA “Research ITalian network on Approximation’.

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  1. Department of Mathematics, University of Padova, Padova, Italy

    Marco Vianello

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  1. Marco Vianello
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Correspondence to Marco Vianello.

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Vianello, M. Subperiodic Dubiner distance, norming meshes and trigonometric polynomial optimization. Optim Lett 12, 1659–1667 (2018). https://doi.org/10.1007/s11590-018-1250-1

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  • DOI: https://doi.org/10.1007/s11590-018-1250-1

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