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Best approximation by ridge functions in L p -spaces

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Ukrainian Mathematical Journal Aims and scope

We study the approximation of the classes of functions by the manifold R n formed by all possible linear combinations of n ridge functions of the form r(a · x)): It is proved that, for any 1 ≤ q ≤ p ≤ ∞, the deviation of the Sobolev class W r p from the set R n of ridge functions in the space L q (B d) satisfies the sharp order n -r/(d-1).

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Authors and Affiliations

  1. Technion, Haifa, Israel

    V. E. Maiorov

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  1. V. E. Maiorov
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 3, pp. 396–408, March, 2010.

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Maiorov, V.E. Best approximation by ridge functions in L p -spaces. Ukr Math J 62, 452–466 (2010). https://doi.org/10.1007/s11253-010-0364-0

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  • DOI: https://doi.org/10.1007/s11253-010-0364-0

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