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Kolmogorov n-Widths of Function Classes Induced by a Non-Degenerate Differential Operator: A Convex Duality Approach

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Abstract

The problem of computing the asymptotic order of the Kolmogorov n-width of the unit ball of the space of multivariate periodic functions induced by a differential operator associated with a polynomial in the general case when the ball is compactly embedded into L 2 has been open for a long time. In the present paper, we use convex analytical tools to solve it in the case when the differential operator is non-degenerate.

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Authors and Affiliations

  1. Sorbonne Universités – UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France

    Patrick L. Combettes

  2. Information Technology Institute, Vietnam National University, Hanoi, Vietnam

    Dinh Dũng

Authors
  1. Patrick L. Combettes
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  2. Dinh Dũng
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Correspondence to Patrick L. Combettes.

Additional information

Dedicated to Lionel Thibault on the occasion of his 65th birthday

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Combettes, P.L., Dũng, D. Kolmogorov n-Widths of Function Classes Induced by a Non-Degenerate Differential Operator: A Convex Duality Approach. Set-Valued Var. Anal 24, 83–99 (2016). https://doi.org/10.1007/s11228-015-0338-3

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  • DOI: https://doi.org/10.1007/s11228-015-0338-3

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